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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,changed
AUTHOR
Seiichi Manyama, Apr 16 2023
STATUS
approved