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<Text-field style="Heading 1" layout="Normal"><Font encoding="UTF-8">n\303\272meros de Stirling,</Font></Text-field>
<Text-field style="Text" layout="Normal"><Font italic="true">n.</Font>  <Font bold="true" encoding="UTF-8">1. n\303\272meros de Stirling de primeira esp\303\251cie.</Font> os inteiros <Font italic="true">s</Font>(<Font italic="true">n</Font>, <Font italic="true">k</Font><Font encoding="UTF-8">) gerados pela defini\303\247\303\243o recursiva: 
</Font><Font italic="true">s</Font>(0, 0)  =  1;    <Font italic="true">s</Font>(<Font italic="true">n</Font>, 0)  =  0   (<Font italic="true">n</Font>&gt;0), 
e, para 0&lt;<Font italic="true">k</Font>&lt;<Font italic="true">n</Font>, 
<Font italic="true"> s</Font>(<Font italic="true">n</Font> + 1, <Font italic="true">k</Font>)  = <Font italic="true">s</Font>(<Font italic="true">n</Font>, <Font italic="true">k</Font> - 1) - <Font italic="true">ns</Font>(<Font italic="true">n</Font>,<Font italic="true"> k</Font>); 
<Font encoding="UTF-8">os primeiros termos desta sequ\303\252ncia s\303\243o mostrados abaixo. 
</Font></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><Image height="146" width="166" zoomable="false">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<Drawing-Root>LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlZztGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiVnOUYqLSUpQ0hJTERSRU5HNiI=</Drawing-Root></Image></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true" encoding="UTF-8">n\303\272meros de Stirling de primeira esp\303\251cie.</Font></Text-field>
<Text-field style="Text" layout="Normal"> <Font bold="true" encoding="UTF-8">2. n\303\272meros de Stirling de segunda esp\303\251cie</Font><Font encoding="UTF-8">, os n\303\272meros naturais </Font><Font italic="true">S</Font>(<Font italic="true">n</Font>,<Font italic="true"> k</Font><Font encoding="UTF-8">) gerados pela defini\303\247\303\243o recursiva: 
</Font><Font italic="true">    S</Font>(<Font italic="true">n</Font>, <Font italic="true">n</Font>)  =  1    (<Font italic="true">n</Font> &gt; 0), 
<Font italic="true">    S</Font>(<Font italic="true">n</Font>, 0)  =  0    (<Font italic="true">n </Font> <Font family="MaplePi" encoding="UTF-8">\302\263</Font> 0), 
e, para 0&lt;<Font italic="true">k</Font>&lt;<Font italic="true">n</Font>, 
<Font italic="true"> S</Font>(<Font italic="true">n</Font> + 1, <Font italic="true">k</Font>)  = <Font italic="true">S</Font>(<Font italic="true">n</Font>, <Font italic="true">k</Font> - 1) + <Font italic="true">kS</Font>(<Font italic="true">n</Font>, <Font italic="true">k</Font>); 
<Font encoding="UTF-8">os primeiros termos desta sequ\303\252ncia s\303\243o mostrados abaixo. Os n\303\272meros de Stirling de segunda esp\303\251cie contam o n\303\272mero de parti\303\247\303\265es de um conjunto </Font><Font italic="true">n-</Font>elemento em precisamente <Font italic="true">k</Font> partes.  
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<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true" encoding="UTF-8">n\303\272meros de Stirling de segunda esp\303\251cie.</Font></Text-field>
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<Font encoding="UTF-8">(Nomeados depois do matem\303\241tico escoc\303\252s, </Font><Font italic="true">James Stirling</Font>, conhecido como <Font encoding="UTF-8" italic="true">Stirling, o V\303\252neto</Font><Font encoding="UTF-8"> (1692-1770), que foi expulso de Oxford em 1715 por seu contato com os Jacobites, e prosseguiu seus estudos em Veneza. Quando retornou \303\240 Gr\303\243-Bretanha, foi eleito </Font><Font bold="true">Fellow</Font> da <Font bold="true">Royal Society</Font><Font encoding="UTF-8">, correspondeu-se com Newton e Maclaurin, e publicou trabalhos em s\303\251ries infinitas e gravita\303\247\303\243o.  Mais tarde, se tornou gerente da Companhia de Minera\303\247\303\243o Escocesa.)</Font></Text-field>
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