A370937 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - log(1+3*x)/3) ).

1, 1, 1, 3, 12, 54, 432, 2862, 29880, 311688, 3530952, 52947432, 694960560, 12339656640, 208855024128, 3885592056624, 84031138091520, 1688108258868480, 41851910546369280, 986544325475565696, 25610732492679696384, 720669291974958124800, 19681263432530494848000

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A198860, A370936.

Programs

Mathematica

a[n_]:=Sum[3^(n-k)*(n+k)!*StirlingS1[n, k],{k,0,n}]/(n+1)!; Array[a,23,0] (* Stefano Spezia, Apr 20 2025 *)

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-log(1+3*x)/3))/x))

PARI

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

Formula

a(n) = (1/(n+1)!) * Sum_{k=0..n} 3^(n-k) * (n+k)! * Stirling1(n,k).