A047792 a(n) = Sum_{k=0..n} Stirling1(n,k)*Stirling2(n,k).

1, 1, 0, -6, 36, 50, -6575, 145222, -1489978, -49083480, 4200404478, -182031111702, 4165517606173, 176264238017452, -33427749628678925, 2913726991238703330, -165770248921085801710, 1422295225609567363172, 1326793746164926878993976

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..295

Crossrefs

Cf. A008275, A008277, A047793, A047794, A047795.

Programs

GAP

List([0..20], n-> Sum([0..n], k-> (-1)^(n-k)*Stirling1(n,k) *Stirling2(n,k) )); # G. C. Greubel, Aug 07 2019

Magma

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

Maple

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

Mathematica

Flatten[{1, Table[Sum[StirlingS1[n, k]*StirlingS2[n, k], {k, n}], {n,20}] }] (* Vaclav Kotesovec, Oct 13 2018 *)

PARI

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

Sage

[sum((-1)^(n-k)*stirling_number1(n,k)*stirling_number2(n,k) for k in (0..n)) for n in (0..20)] # G. C. Greubel, Aug 07 2019