OFFSET
0,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..300
FORMULA
E.g.f.: 1/(1-LambertW(-x)^4)^(1/4). - Vaclav Kotesovec, Sep 01 2014
a(n) ~ n^(n-3/8) * (sqrt(Pi) / (2^(1/8) * Gamma(1/8))) * (1 - 11 * sqrt(2/n) * Gamma(1/8) / (64 * Gamma(5/8))). - Vaclav Kotesovec, Sep 01 2014
MAPLE
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(i>n, 0, add(b(n-i*j, i+4)*(i-1)!^j*
multinomial(n, n-i*j, i$j)/j!, j=0..n/i)))
end:
a:= a->add(b(j, 4)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..20);
MATHEMATICA
CoefficientList[Series[1/(1-LambertW[-x]^4)^(1/4), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Sep 01 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 31 2014
STATUS
approved