A376383 Expansion of e.g.f. ( (1/x) * Series_Reversion( x*(1 - x*(exp(x) - 1))^3 ) )^(2/3).
1, 0, 4, 6, 368, 2170, 119712, 1542254, 86459200, 1884526578, 111718563680, 3566361530182, 227778981600480, 9716705596149578, 674774811779124448, 36153388845386205150, 2740217544109113107072, 176542121944523097148642, 14610965831419986026094816
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x*(1-x*(exp(x)-1))^3)/x)^(2/3))) -
PARI
a(n) = 2*n!*sum(k=0, n\2, (3*n+k+1)!*stirling(n-k, k, 2)/(n-k)!)/(3*n+2)!;
Formula
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A371273.
a(n) = (2 * n!/(3*n+2)!) * Sum_{k=0..floor(n/2)} (3*n+k+1)! * Stirling2(n-k,k)/(n-k)!.