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

0,3

Links

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A367156.

Sequence in context: A166547 A156204 A231519 * A197447 A202780 A297804

Adjacent sequences: A367154 A367155 A367156 * A367158 A367159 A367160

Keyword

nonn

Author

Seiichi Manyama, Nov 07 2023

Status

approved