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A362351
a(n) = n! * Sum_{k=0..floor(n/3)} (k/6)^k / (k! * (n-3*k)!).
5
1, 1, 1, 2, 5, 11, 61, 316, 1177, 11005, 84121, 434446, 5642781, 56725527, 374014005, 6211205456, 77331975281, 620174850521, 12539310726577, 186125334960730, 1757911008913141, 41887694462674691, 721886016954223661, 7846403629258814852, 215270385425700640905
OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: exp(x) / (1 + LambertW(-x^3/6)).
a(n) ~ n^n * (exp(6^(1/3)*exp(-1/3)) + 2*cos(2^(-2/3)*3^(5/6)*exp(-1/3) - 2*Pi*n/3) / exp(2^(-2/3)*3^(1/3)*exp(-1/3))) / (2^(n/3) * 3^(n/3 + 1/2) * exp(2*n/3)). - Vaclav Kotesovec, Apr 18 2023
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(-x^3/6))))
CROSSREFS
Cf. A362173.
Sequence in context: A140547 A131480 A262228 * A213073 A267527 A286453
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 17 2023
STATUS
approved