A377554 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x*exp(x))^3 ).
1, 3, 30, 537, 14124, 493695, 21601458, 1137294039, 70064934600, 4947238170747, 394022075650590, 34951812094581723, 3417754921150904172, 365287875167708973831, 42368411854713294141834, 5300422308901745571018735, 711465905597330333014408848, 101995745742232833085109746803
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, k^(n-k)*binomial(3*n+3, k)/(n-k)!)/(n+1);
Formula
E.g.f. satisfies A(x) = (1 + x * A(x) * exp(x*A(x)))^3.
E.g.f.: B(x)^3, where B(x) is the e.g.f. of A364986.
a(n) = (n!/(n+1)) * Sum_{k=0..n} k^(n-k) * binomial(3*n+3,k)/(n-k)!.