A365015 E.g.f. satisfies A(x) = exp( x*A(x)^3/(1 - x * A(x)) ).

1, 1, 9, 154, 3997, 140216, 6217549, 333774064, 21051514425, 1526073116032, 125040978948241, 11428407889500416, 1152792683163827413, 127215353330004610048, 15246125111980753585365, 1971966282368187450198016, 273796236099258954747416689

Offset: 0

Author

Seiichi Manyama, Aug 15 2023

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..327

Crossrefs

Cf. A361066, A361094, A365016.

Programs

Mathematica

Array[#!*Sum[ (# + 2 k + 1)^(k - 1)*Binomial[# - 1, # - k]/k!, {k, 0, #}] &, 17, 0] (* Michael De Vlieger, Aug 18 2023 *)

PARI

a(n) = n!*sum(k=0, n, (n+2*k+1)^(k-1)*binomial(n-1, n-k)/k!);

Formula

a(n) = n! * Sum_{k=0..n} (n+2*k+1)^(k-1) * binomial(n-1,n-k)/k!.