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A362336
a(n) = n! * Sum_{k=0..floor(n/5)} (n/120)^k /(k! * (n-5*k)!).
2
1, 1, 1, 1, 1, 6, 37, 148, 449, 1135, 15121, 172789, 1207009, 6106816, 24748725, 510855346, 8524169473, 84981641837, 602009065729, 3357322881625, 93871272204481, 2059974308136466, 26683062726210661, 243032907824598816, 1725747644222610625
OFFSET
0,6
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = n! * [x^n] exp(x + n*x^5/120).
E.g.f.: exp( ( -24*LambertW(-x^5/24) )^(1/5) ) / (1 + LambertW(-x^5/24)).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((-24*lambertw(-x^5/24))^(1/5))/(1+lambertw(-x^5/24))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 16 2023
STATUS
approved