A376766 a(n) = 1 + Sum_{k=1..n, j=1..k} binomial(n,k)*binomial(n,j)*|Stirling_1(k,j)|*j!.

1, 2, 9, 67, 709, 9766, 165751, 3342081, 78023905, 2069303986, 61440372701, 2018742611535, 72713594116285, 2848845086153782, 120610707912196867, 5486918880456879061, 266925386719765703169, 13827085272988988990146, 759855686741314297312177, 44152359275709028329389627

Offset: 0

Author

Peter J. Cameron, Nov 03 2024

Keywords

• nonn

Comments

If Stirling_1 in the definition is changed to Stirling_2, we get A000169.

Links

• Paolo Xausa, Table of n, a(n) for n = 0..375

Crossrefs

Cf. A000169, A000312, A002720, A007840, A376765.

Programs

Maple

A376766 := proc(n) local k,j;
1 + sum(sum(binomial(n,k)*binomial(n,j)*abs(stirling1(k,j))*j!,j=1..k),k=1..n);
end; # N. J. A. Sloane, Nov 03 2024

Mathematica

A376766[n_] := 1 + Sum[Binomial[n, k]*Binomial[n, j]*Abs[StirlingS1[k, j]]*j!, {k, n}, {j, k}];
Array[A376766, 25, 0] (* Paolo Xausa, Nov 04 2024 *)

Formula

a(n) ~ c * d^n * n^n / exp(n), where d = A226572 = -LambertW(-1, -exp(-2)) and c = 1.350274261169912007066341887216772613236351893372220769387... - Vaclav Kotesovec, Nov 09 2024

Extensions

Definition corrected by N. J. A. Sloane, Nov 09 2024