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URL: https://oeis.org/A371021

⇱ A371021 - OEIS

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A371021
Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x^3/6*exp(x)) ).
0
1, 0, 0, 1, 4, 10, 80, 1015, 9016, 80724, 1092120, 16872405, 246966940, 3932454526, 73869476044, 1485097614455, 30688224287280, 682450482838440, 16508839426673136, 420562937260614249, 11193327347979937140, 315276822746559147250, 9383980947735649740100
OFFSET
0,5
FORMULA
a(n) = (n!/(n+1)) * Sum_{k=0..floor(n/3)} k^(n-3*k) * binomial(n+1,k)/(6^k * (n-3*k)!).
MATHEMATICA
Join[{1}, Table[(n!/(n + 1))*Sum[k^(n - 3*k)*Binomial[n + 1, k]/(6^k*(n - 3*k)!), {k, 0, Floor[n/3]}], {n, 30}]] (* Wesley Ivan Hurt, Aug 05 2025 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1+x^3/6*exp(x)))/x))
(PARI) a(n) = n!*sum(k=0, n\3, k^(n-3*k)*binomial(n+1, k)/(6^k*(n-3*k)!))/(n+1);
CROSSREFS
Sequence in context: A239502 A171754 A215872 * A059919 A143047 A156329
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 08 2024
STATUS
approved