A155207 G.f.: A(x) = exp( Sum_{n>=1} 4^(n^2) * x^n/n ), a power series in x with integer coefficients.

1, 4, 136, 87904, 1074100576, 225184288253824, 787061981348092400896, 45273238870711805132010916864, 42535296046210357883346895894694749696, 649556283428320264374891976653586736162144180224

Offset: 0

Author

Paul D. Hanna, Feb 04 2009

Keywords

• nonn

Comments

More generally, for m integer, exp( Sum_{n>=1} m^(n^2) * x^n/n ) is a power series in x with integer coefficients.

Examples

			G.f.: A(x) = 1 + 4*x + 136*x^2 + 87904*x^3 + 1074100576*x^4 +...
log(A(x)) = 4*x + 4^4*x^2/2 + 4^9*x^3/3 + 4^16*x^4/4 + 4^25*x^5/5 +...
		

Crossrefs

Cf. A060757, A155208, A155209, A155210, variants: A155200, A155203.

Programs

PARI

{a(n)=polcoeff(exp(sum(m=1,n+1,4^(m^2)*x^m/m)+x*O(x^n)),n)}

Formula

G.f. satisfies: A'(x)/A(x) = 4 + 64*x*A'(16*x)/A(16*x). - Paul D. Hanna, Nov 15 2022

a(n) ~ 4^(n^2)/n. - Vaclav Kotesovec, Oct 31 2024