A371006 Expansion of e.g.f. (1/x) * Series_Reversion( x/(3*exp(x) - 2) ).

1, 3, 21, 246, 4143, 91938, 2543457, 84476766, 3278575515, 145703001450, 7299102908613, 407061606983430, 25016221521245703, 1679926053870309378, 122399565517464024009, 9617404242454811783598, 810684382032520533507891, 72976185712308646408856538

Offset: 0

Author

Seiichi Manyama, Mar 08 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A000272, A371005.

Cf. A371007.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(3*exp(x)-2))/x))

PARI

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

Formula

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

a(n) = n! * Sum_{k=0..n} 3^k * Stirling2(n,k)/(n-k+1)!. - Seiichi Manyama, Nov 07 2024