A379846 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x) / (1 + x*exp(2*x)) ).
1, 2, 15, 202, 3993, 104896, 3449431, 136490768, 6319722513, 335372124160, 20074806151551, 1338341234648320, 98356732036224745, 7900673166769620992, 688709957632464564231, 64754459774124307019776, 6532479591772426224737697, 703834470938326183482621952
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, (3*n-2*k+1)^k*binomial(n+1, n-k)/k!)/(n+1);
Formula
a(n) = (n!/(n+1)) * Sum_{k=0..n} (3*n-2*k+1)^k * binomial(n+1,n-k)/k!.
E.g.f. A(x) satisfies A(x) = exp(x*A(x)) / ( 1 - x*exp(3*x*A(x)) ). - Seiichi Manyama, Feb 04 2025