A338377 G.f. satisfies: A(x) = (1 + x * d/dx(x*A(x)) )^n.

1, 1, 9, 226, 10745, 811026, 88058362, 12920344256, 2453913830097, 584608650175630, 170543970449421371, 59769169004510011674, 24775053368568412720967, 11989194513429991057937296, 6698670769128767044654361520, 4280089524780608663200103685056, 3101341801862271814724389007080481

Offset: 0

Author

Vaclav Kotesovec, Oct 23 2020

Keywords

• nonn

Examples

			a(2) = A113662(2) = 9
a(3) = A113663(3) = 226
a(4) = A113664(4) = 10745
a(5) = A113665(5) = 811026
a(6) = A113666(6) = 88058362
a(7) = A113667(7) = 12920344256
a(8) = A113668(8) = 2453913830097
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..220

Crossrefs

Cf. A113662, A113663, A113664, A113665, A113666, A113667, A113668.

Programs

PARI

{a(n)=local(A=1+x*O(x^n)); for(i=1, n, A=(1+x*deriv(x*A))^n); polcoeff(A, n, x)}
for(n=0, 20, print1(a(n), ", "))

Formula

G.f. satisfies: A(x) = (1 + x * A(x) + x^2 * A'(x) )^n.

a(n) ~ A238223 * exp(1) * n! * n^(n + 1 - 1/n).

a(n) ~ A238223 * exp(1) * n^(n+1) * n! * (1 - log(n)/n).