A341728 Column 1 of A341725.

1, 6, 39, 324, 3365, 41958, 610351, 10146888, 189775017, 3943689930, 90148635203, 2248040395692, 60731103481789, 1766863166037102, 55075428554246295, 1831224444159278736, 64692540643308320081, 2419861007021854813074, 95544948688075940395627

Offset: 1

Author

N. J. A. Sloane, Mar 04 2021

Keywords

• nonn

Crossrefs

Cf. A000557, A005923, A341725, A341726, A341727.

Programs

Maple

A341728 := n -> add((n-k)*binomial(n, k)add(j!*combinat[fibonacci](j+2)*Stirling2(k,j), j=0..k), k=0..n):seq(A341728(n), n=1.. 19); # Mélika Tebni, Sep 04 2023
# E.g.f. Maple program:
A341728 := series(x*exp(x) / (1 - 2*sinh(x)), x = 0, 20):
seq(n!*coeff(A341728, x, n), n = 1 .. 19); # Mélika Tebni, Sep 04 2023

Formula

From Mélika Tebni, Sep 04 2023: (Start)

a(n) = n*A005923(n-1).

E.g.f.: x*exp(x) / (1 - 2*sinh(x)).

a(n) = Sum_{k=0..n} (n-k)*binomial(n, k)*A000557(k). (End)

Extensions

More terms from Mélika Tebni, Sep 04 2023