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

0,3

Links

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

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 *)

Prog

(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
(Magma) [(&+[Binomial(n, k)*StirlingSecond(n, k)^2: k in [0..n]]): n in [0..20]]; // 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
(GAP) List([0..20], n-> Sum([0..n], k-> Binomial(n, k)*Stirling2(n, k)^2 )); # G. C. Greubel, Aug 07 2019

Crossrefs

Cf. A008277, A047799, A211210, A317274.

Sequence in context: A123818 A087591 A061053 * A349038 A126346 A142999

Adjacent sequences: A047795 A047796 A047797 * A047799 A047800 A047801

Keyword

nonn

Author

N. J. A. Sloane

Status

approved