A247329 a(n) = Sum_{k=0..n} (-1)^(n-k) * C(n,k) * Stirling1(n+1, k+1).

1, 2, 9, 58, 475, 4666, 53116, 684762, 9833391, 155341258, 2673209561, 49717424868, 992847765988, 21172798741316, 479921234767976, 11516219861132586, 291523666535143823, 7761036379846481206, 216699016885046232187, 6330257697841339549706, 193043926318644060255531

Offset: 0

Author

Paul D. Hanna, Sep 26 2014

Keywords

• nonn

Examples

			Illustration of initial terms:
a(0) = 1*1 = 1 ;
a(1) = 1*1 + 1*1 = 2 ;
a(2) = 1*2 + 2*3 + 1*1 = 9 ;
a(3) = 1*6 + 3*11 + 3*6 + 1*1 = 58 ;
a(4) = 1*24 + 4*50 + 6*35 + 4*10 + 1*1 = 475 ;
a(5) = 1*120 + 5*274 + 10*225 + 10*85 + 5*15 + 1*1 = 4666 ;
a(6) = 1*720 + 6*1764 + 15*1624 + 20*735 + 15*175 + 6*21 + 1*1 = 53116 ;
a(7) = 1*5040 + 7*13068 + 21*13132 + 35*6769 + 35*1960 + 21*322 + 7*28 + 1*1 = 684762 ; ...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..435

Crossrefs

Cf. A008275 (Stirling1 numbers), A211210.

Programs

Maple

f:= proc(n) local k; add((-1)^(n-k)*binomial(n,k)*Stirling1(n+1,k+1),k=0..n); end proc:
map(f, [$0..30]); # Robert Israel, Aug 01 2019

Mathematica

Table[Sum[(-1)^(n-k) * Binomial[n,k] * StirlingS1[n+1, k+1],{k,0,n}],{n,0,20}] (* Vaclav Kotesovec, Sep 29 2014 *)

PARI

{Stirling1(n, k)=if(n==0, 1, n!*polcoeff(binomial(x, n), k))}
{a(n)=sum(k=0, n, (-1)^(n-k)*binomial(n,k)*Stirling1(n+1, k+1))}
for(n=0,30,print1(a(n),", "))