OFFSET
0,7
COMMENTS
Number of labeled ordered partitions of an n-set into odd parts > 1.
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
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}]
PROG
(PARI) seq(n)={Vec(serlaplace(1 / (1 + x - sinh(x + O(x*x^n)))))} \\ Andrew Howroyd, Feb 08 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 08 2020
STATUS
approved