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Revision History for A155207

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

#4 by Paul D. Hanna at Tue Nov 15 00:59:02 EST 2022

STATUS

editing

approved

#3 by Paul D. Hanna at Tue Nov 15 00:59:00 EST 2022

FORMULA

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

STATUS

approved

editing

#2 by Russ Cox at Fri Mar 30 18:37:15 EDT 2012

AUTHOR

_Paul D. Hanna (pauldhanna(AT)juno.com), _, Feb 04 2009

Discussion

Fri Mar 30

18:37

OEIS Server: https://oeis.org/edit/global/213

#1 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

NAME

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

DATA

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.

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.

KEYWORD

nonn,new

AUTHOR

Paul D. Hanna (pauldhanna(AT)juno.com), Feb 04 2009

STATUS

approved