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A155203
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G.f.: A(x) = exp( Sum_{n>=1} 3^(n^2) * x^n/n ), a power series in x with integer coefficients.
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11
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OFFSET
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0,2
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COMMENTS
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More generally, for m integer, exp( Sum_{n>=1} m^(n^2) * x^n/n ) is a power series in x with integer coefficients.
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LINKS
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Table of n, a(n) for n=0..9.
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FORMULA
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Equals column 0 of triangle A155812.
G.f. satisfies: A'(x)/A(x) = 3 + 27*x*A'(9*x)/A(9*x). - Paul D. Hanna, Nov 15 2022
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EXAMPLE
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G.f.: A(x) = 1 + 3*x + 45*x^2 + 6687*x^3 + 10782369*x^4 + 169490304819*x^5 +...
log(A(x)) = 3*x + 3^4*x^2/2 + 3^9*x^3/3 + 3^16*x^4/4 + 3^25*x^5/5 +...
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PROG
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(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, 3^(m^2)*x^m/m)+x*O(x^n)), n)}
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CROSSREFS
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Cf. A155204, A155205, A155206, A155812 (triangle), variants: A155200, A155207.
Sequence in context: A265621 A124488 A086683 * A183131 A037105 A196137
Adjacent sequences: A155200 A155201 A155202 * A155204 A155205 A155206
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Feb 04 2009
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STATUS
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approved
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