A365014 E.g.f. satisfies A(x) = exp( x*A(x)^2/(1 - x * A(x)^3) ).

1, 1, 7, 103, 2349, 72961, 2874793, 137399487, 7724650601, 499542475105, 36532938744621, 2981405776356679, 268605245211618637, 26480489709604968129, 2835590837094928349921, 327748240537910056251151, 40669893396736296241364817, 5392699633877586027282801217

Offset: 0

Author

Seiichi Manyama, Aug 15 2023

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..332

Crossrefs

Cf. A361093, A361142.

Programs

Mathematica

Array[#!*Sum[ (3 # - k + 1)^(k - 1)*Binomial[# - 1, # - k]/k!, {k, 0, #}] &, 18, 0] (* Michael De Vlieger, Aug 18 2023 *)

PARI

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

Formula

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