A341727 Column 1 of A341724.

1, -4, 24, -200, 2080, -25932, 377216, -6271120, 117287424, -2437334420, 55714920448, -1389365372760, 37533886128128, -1091981490075868, 34038486791454720, -1131758947520249120, 39982188936149204992, -1495556350390047594276, 59050025742595595436032

Offset: 1

Author

N. J. A. Sloane, Mar 04 2021

Keywords

• sign

Crossrefs

Cf. A000556, A000557, A341724 ,A341726, A341728.

Programs

Maple

A341727 := n -> (-1)^(n-1)*n*add(k!*combinat[fibonacci](k+2)*Stirling2(n-1, k), k=0..n-1):seq(A341727(n), n = 1 .. 19); # Mélika Tebni, Sep 04 2023
# E.g.f. Maple program:
A341727 := series(x / (1 + 2*sinh(x)), x = 0, 20):
seq(n!*coeff(A341727, x, n), n = 1 .. 19); # Mélika Tebni, Sep 04 2023

Formula

From Mélika Tebni, Sep 04 2023: (Start)

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

a(n) = (-1)^(n-1)*n*A000557(n-1).

a(n) = (-1)^(n-1)*Sum_{k=0..n} A000556(k)*(n-k)*binomial(n, k). (End)

Extensions

More terms from Mélika Tebni, Sep 04 2023