A076901 E.g.f.: 1/Product_{m>0} (1+(-x)^m/m!).

1, 1, 1, 4, 21, 96, 520, 3795, 32053, 284368, 2763876, 30648465, 373339824, 4833294389, 67167087793, 1009753574739, 16215467043493, 275361718915824, 4947532173402532, 94054153646919213, 1882793796608183356, 39528099512321898363, 869222284280777733043

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..200

Formula

a(n) ~ c * n!, where c = Product_{k>=2} (1 + (-1)^k/k!) = 0.773515873861910082... - Vaclav Kotesovec, Sep 14 2017

Maple

A076901 := proc(n) local a, s;
s := proc(n) local d; add((-1)^d*n!/(d*(n/d)!^d),
d = numtheory[divisors](n)) end:
a := proc(n) option remember; local k;
`if`(n=0, 1, add(binomial(n-1, k-1)*s(k)*a(n-k), k = 1..n)) end:
(-1)^n*a(n) end:
seq(A076901(n), n=0..20);  # Peter Luschny, Apr 16 2011

Mathematica

nmax = 25; Table[SeriesCoefficient[Product[1/(1 + (-x)^k/k!), {k, 1, n}], {x, 0, n}], {n, 0, nmax}] * Range[0, nmax]! (* Vaclav Kotesovec, Sep 14 2017 *)

Crossrefs

Cf. A005651, A182928.

Sequence in context: A231377 A017967 A292308 * A080043 A240456 A113022

Adjacent sequences: A076898 A076899 A076900 * A076902 A076903 A076904

Keyword

nonn

Author

Vladeta Jovovic, Nov 26 2002

Status

approved