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

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = (n!/(n+1)) * Sum_{k=0..n} (3*n-2*k+1)^k * binomial(n+1,n-k)/k!.

Prog

(PARI) a(n) = n!*sum(k=0, n, (3*n-2*k+1)^k*binomial(n+1, n-k)/k!)/(n+1);

Crossrefs

Cf. A379456, A379847.

Cf. A366232, A379701.

Sequence in context: A221102 A351920 A319466 * A020557 A323118 A184361

Adjacent sequences: A379843 A379844 A379845 * A379847 A379848 A379849

Keyword

nonn

Author

Seiichi Manyama, Jan 04 2025

Status

approved