A367163 E.g.f. satisfies A(x) = 1 + A(x)^3 * (exp(x*A(x)) - 1).

1, 1, 9, 160, 4367, 161796, 7592593, 431826760, 28875060411, 2220199609420, 193010401410437, 18720726373805952, 2004328775014537111, 234797380878372574276, 29873926565253226992921, 4102473564838214815027576, 604804589755948599369229811

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = Sum_{k=0..n} (n+3*k)!/(n+2*k+1)! * Stirling2(n,k).

Prog

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

Crossrefs

Cf. A000272, A052894, A367162.

Sequence in context: A309472 A060348 A365016 * A363479 A217392 A327978

Adjacent sequences: A367160 A367161 A367162 * A367164 A367165 A367166

Keyword

nonn

Author

Seiichi Manyama, Nov 07 2023

Status

approved