A370908 Expansion of e.g.f. (1/x) * Series_Reversion( 4*x/(3 + exp(4*x)) ).

1, 1, 6, 58, 824, 15576, 368560, 10494352, 349680000, 13354956160, 575343613184, 27606884967168, 1460295317318656, 84429863673895936, 5297505756426098688, 358520710389920598016, 26033795963713021116416, 2019060825791610516504576

Offset: 0

Author

Seiichi Manyama, Mar 05 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A201595, A370907.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(4*x/(3+exp(4*x)))/x))

PARI

a(n) = sum(k=0, n+1, 3^(n+1-k)*k^n*binomial(n+1, k))/(4*(n+1));

Formula

a(n) = 1/(4*(n+1)) * Sum_{k=0..n+1} 3^(n+1-k) * k^n * binomial(n+1,k).

a(n) = n! * Sum_{k=0..n} 4^(n-k) * Stirling2(n,k)/(n-k+1)!. - Seiichi Manyama, Nov 07 2024