A332258 E.g.f.: 1 / (1 + x - sinh(x)).

1, 0, 0, 1, 0, 1, 20, 1, 112, 1681, 492, 27721, 371624, 319177, 13461604, 171387217, 319071456, 11466038689, 143550642140, 484491620089, 15758152572952, 199089883272217, 1077471975974484, 32827750137627457, 427744154995090256, 3385134777669637681

Offset: 0

Author

Ilya Gutkovskiy, Feb 08 2020

Keywords

• nonn

Comments

Number of labeled ordered partitions of an n-set into odd parts > 1.

Crossrefs

Cf. A006154, A009227, A032032.

Programs

Mathematica

nmax = 25; CoefficientList[Series[1/(1 + x - Sinh[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 2 k - 1] a[n - 2 k + 1], {k, 2, Ceiling[n/2]}]; Table[a[n], {n, 0, 25}]

PARI

seq(n)={Vec(serlaplace(1 / (1 + x - sinh(x + O(x*x^n)))))} \\ Andrew Howroyd, Feb 08 2020

Formula

a(0) = 1; a(n) = Sum_{k=2..ceiling(n/2)} binomial(n,2*k-1) * a(n-2*k+1).

a(n) ~ n! / ((cosh(r) - 1) * r^(n+1)), where r = 1.72911689821437486498840709347... is the root of the equation 1 + r - sinh(r) = 0. - Vaclav Kotesovec, Feb 08 2020