OFFSET
0,6
FORMULA
E.g.f.: Product_{k>0} exp(x^(4*k-3)).
a(n) ~ exp(1/4 + sqrt(n) - n) * n^(n-1/4) / 2. - Vaclav Kotesovec, Oct 11 2017
a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n-1,4*k) * (4*k+1)! * a(n-4*k-1). - Ilya Gutkovskiy, Feb 24 2022
a(n) = n! * Sum_{k=0..floor(n/4)} binomial(n-3*k-1,k)/(n-4*k)!. - Seiichi Manyama, Jun 08 2024
MATHEMATICA
CoefficientList[Series[E^(x/(1 - x^4)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Oct 11 2017 *)
PROG
(PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(x/(1-x^4))))
(PARI) N=66; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, exp(x^(4*k-3)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 10 2017
STATUS
approved