login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A362321
a(n) = n! * Sum_{k=0..floor(n/4)} n^k /(k! * (n-4*k)!).
2
1, 1, 1, 1, 97, 601, 2161, 5881, 1303681, 14723857, 90770401, 402581521, 139389608161, 2284512533161, 19946635524817, 122623661651401, 57728368477678081, 1240234284406887841, 14010634784751445441, 110117252571345122977
OFFSET
0,5
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = n! * [x^n] exp(x + n*x^4).
E.g.f.: exp( ( -LambertW(-4*x^4)/4 )^(1/4) ) / (1 + LambertW(-4*x^4)).
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((-lambertw(-4*x^4)/4)^(1/4))/(1+lambertw(-4*x^4))))
CROSSREFS
Sequence in context: A142765 A144130 A144131 * A130833 A130873 A193411
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 16 2023
STATUS
approved