A047795 a(n) = Sum_{k=0..n} C(n,k)*Stirling1(n,k)*Stirling2(n,k).

1, 1, -1, -20, 295, 871, -196784, 6287772, 29169631, -18200393741, 1304183716981, -27109895360074, -6212943553813622, 1062831339757496245, -85292203894284124100, -1487854700305245210924, 1896933688279584387159631, -377233175400513002923379973

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..280

Crossrefs

Cf. A008275, A008277, A047792, A047793, A047794.

Programs

GAP

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

Magma

[(&+[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(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]*StirlingS1[n, k]*StirlingS2[n, k], {k, 0, n}], {n, 0, 20}] (* G. C. Greubel, Aug 07 2019 *)

PARI

{a(n) = sum(k=0,n,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((-1)^(n-k)*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