A370878 Expansion of e.g.f. (1/x) * Series_Reversion( x/(x + exp(x^3/6)) ).
1, 1, 2, 7, 40, 320, 3190, 37870, 526400, 8434720, 153092800, 3099958400, 69237737800, 1691184094600, 44855672061200, 1283910696468400, 39445370739174400, 1294688750568012800, 45213628130719048000, 1673957726914620347200, 65493419262155812928000
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(x+exp(x^3/6)))/x)) -
PARI
a(n) = n!*sum(k=0, n\3, (3*k+1)^(k-1)*binomial(n, 3*k)/(6^k*k!));
Formula
a(n) = n! * Sum_{k=0..floor(n/3)} (3*k+1)^(k-1) * binomial(n,3*k)/(6^k * k!).