A382039 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(3*x)) ).

1, 1, 10, 147, 3252, 96165, 3569778, 159771717, 8378589096, 504057519945, 34227869887710, 2589957885708369, 216121694333055228, 19717935804239270013, 1952741002119283320714, 208629930642065967641805, 23919711023929511941080912, 2929406351866509691077727761

Offset: 0

Author

Seiichi Manyama, Mar 13 2025

Keywords

• nonn

Crossrefs

Cf. A213644, A379690, A382040.

Cf. A366233.

Programs

PARI

a(n) = sum(k=0, n, (3*k)^(n-k)*(n+k)!/(k!*(n-k)!))/(n+1);

Formula

E.g.f. A(x) satisfies A(x) = 1 + x*A(x)^2*exp(3*x*A(x)).

a(n) = (1/(n+1)) * Sum_{k=0..n} (3*k)^(n-k) * (n+k)!/(k! * (n-k)!).