A047798 a(n) = Sum_{k=0..n} C(n,k)*Stirling2(n,k)^2.

1, 1, 3, 31, 443, 9006, 241147, 7956579, 318973867, 15061651528, 824029357046, 51526959899570, 3636995712432667, 287053182699020609, 25126145438688593769, 2421761360666327615911, 255466264644678162575691, 29336098320197429601856772

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A008277, A047799, A211210, A317274.

Programs

GAP

List([0..20], n-> Sum([0..n], k-> Binomial(n,k)*Stirling2(n,k)^2 )); # G. C. Greubel, Aug 07 2019

Magma

[(&+[Binomial(n,k)*StirlingSecond(n,k)^2: k in [0..n]]): n in [0..20]]; // G. C. Greubel, Aug 07 2019

Maple

seq(add(binomial(n,k)*stirling2(n, k)^2, k = 0..n), n = 0..20); # G. C. Greubel, Aug 07 2019

Mathematica

Table[Sum[Binomial[n, k]*StirlingS2[n, k]^2, {k,0,n}], {n,0,20}] (* G. C. Greubel, Aug 07 2019 *)

PARI

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

Sage

[sum(binomial(n,k)*stirling_number2(n,k)^2 for k in (0..n)) for n in (0..20)] # G. C. Greubel, Aug 07 2019