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A362319
a(n) = n! * Sum_{k=0..floor(n/5)} (n/5)^k / (k! * (n-5*k)!).
6
1, 1, 1, 1, 1, 121, 865, 3529, 10753, 27217, 7318081, 96720625, 689990401, 3508289929, 14239793569, 5933573525881, 114415115802625, 1165402803391009, 8298505279241857, 46355961619888993, 26167218073714552321, 663290722580370585625
OFFSET
0,6
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = n! * [x^n] exp(x + n*x^5/5).
E.g.f.: exp( ( -LambertW(-x^5) )^(1/5) ) / (1 + LambertW(-x^5)).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((-lambertw(-x^5))^(1/5))/(1+lambertw(-x^5))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 16 2023
STATUS
approved