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Formula:8540

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Digital Library of Mathematical Functions ID 26.8.E19

( k h ) ⁢ s ⁡ ( n , k ) = ∑ j = k - h n - h ( n j ) ⁢ s ⁡ ( n - j , h ) ⁢ s ⁡ ( j , k - h ) , binomial 𝑘 ℎ Stirling-number-first-kind-S 𝑛 𝑘 superscript subscript 𝑗 𝑘 ℎ 𝑛 ℎ binomial 𝑛 𝑗 Stirling-number-first-kind-S 𝑛 𝑗 ℎ Stirling-number-first-kind-S 𝑗 𝑘 ℎ {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{k}{h}s\left(n,k\right)=% \sum_{j=k-h}^{n-h}\genfrac{(}{)}{0.0pt}{}{n}{j}s\left(n-j,h\right)s\left(j,k-h% \right),}}


Constraint(s)

n ≥ k ≥ h 𝑛 𝑘 ℎ {\displaystyle{\displaystyle n\geq k\geq h}}

Symbols List

  • s ⁡ ( n , k ) Stirling-number-first-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle s\left(\NVar{n},\NVar{k}\right)}} :
  • ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}} :
  • h ℎ {\displaystyle{\displaystyle h}} : nonnegative integer
  • j 𝑗 {\displaystyle{\displaystyle j}} : nonnegative integer
  • k 𝑘 {\displaystyle{\displaystyle k}} : nonnegative integer
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
  •  Edit this on Wikidata

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This page was last edited on 28 January 2024, at 10:30.
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