A380973 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x*exp(3*x)) ).
1, 1, 9, 115, 2213, 56781, 1825735, 70718383, 3207565737, 166830072409, 9791107408331, 640182529765395, 46152280917472669, 3637314366894167077, 311129703773921407887, 28708644100373375591191, 2842495895373573092038865, 300611288206029730901431473, 33820062046972635799385887123
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, (3*k)^(n-k)*(n+1)^(k-1)*binomial(n, k));
Formula
E.g.f. A(x) satisfies A(x) = exp( x*A(x) * exp(3*x*A(x)) ).
a(n) = Sum_{k=0..n} (3*k)^(n-k) * (n+1)^(k-1) * binomial(n,k).