A047794 a(n) = Sum_{k=0..n} C(n,k)*|Stirling1(n,k)*Stirling2(n,k)|.

1, 1, 3, 34, 631, 16871, 617356, 28968990, 1680536159, 117572734195, 9715771690081, 932711356031016, 102653506699902874, 12810868034079756421, 1795954763065584594656, 280569433733767673934426, 48506369621902094002862671, 9224242346164172284054561019

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..275

Crossrefs

Cf. A008275, A008277, A047792, A047793, A047795.

Programs

GAP

List([0..20], n-> Sum([0..n], k-> Stirling1(n,k)*Stirling2(n,k) *Binomial(n,k) )); # G. C. Greubel, Aug 07 2019

Magma

[(&+[(-1)^(n-k)*StirlingFirst(n,k)*StirlingSecond(n,k) *Binomial(n,k): k in [0..n]]): n in [0..20]]; // G. C. Greubel, Aug 07 2019

Maple

seq(add((-1)^(n-k)*binomial(n, k)*stirling1(n, k)*stirling2(n, k), k = 0 .. n), n = 0..20); # G. C. Greubel, Aug 07 2019

Mathematica

Table[Sum[Binomial[n,k]Abs[StirlingS1[n,k]StirlingS2[n,k]],{k,0,n}],{n,0,20}] (* Harvey P. Dale, Apr 10 2012 *)

PARI

{a(n) = sum(k=0,n, (-1)^(n-k)*stirling(n,k,1)*stirling(n,k,2) *binomial(n,k))};
vector(20, n, n--; a(n)) \\ G. C. Greubel, Aug 07 2019

Sage

[sum(stirling_number1(n,k)*stirling_number2(n,k)*binomial(n,k) for k in (0..n)) for n in (0..20)] # G. C. Greubel, Aug 07 2019