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

0,2

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.

Links

Table of n, a(n) for n=0..9.

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

Example

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 +...

Prog

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

Crossrefs

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

Sequence in context: A366446 A001374 A229416 * A201388 A089666 A363114

Adjacent sequences: A155204 A155205 A155206 * A155208 A155209 A155210

Keyword

nonn

Author

Paul D. Hanna, Feb 04 2009

Status

approved