A367157 E.g.f. satisfies A(x) = 1 + A(x)^3 * log(1 + x*A(x)).

1, 1, 7, 107, 2528, 81324, 3317958, 164182458, 9555617008, 639681044040, 48424744784136, 4090543382765520, 381452559291894864, 38923292146836546864, 4313976527840736485280, 516083186352589573976208, 66281598254535375499398144, 9096262997259437367544137984

Offset: 0

Author

Seiichi Manyama, Nov 07 2023

Keywords

• nonn

Crossrefs

Cf. A367156.

Programs

Mathematica

Table[Sum[(n+3*k)!/(n+2*k+1)! * StirlingS1[n,k], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 10 2023 *)

PARI

a(n) = sum(k=0, n, (n+3*k)!/(n+2*k+1)!*stirling(n, k, 1));

Formula

a(n) = Sum_{k=0..n} (n+3*k)!/(n+2*k+1)! * Stirling1(n,k).