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Search: id:A155204
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| A155204 |
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G.f.: A(x) = exp( Sum_{n>=1} (3^n + 1)^n * x^n/n ), a power series in x with integer coefficients. |
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+0
8
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| 1, 4, 58, 7528, 11333974, 173018964568, 25223063625377572, 34295288559321731710864, 429734241619476967064512081894, 49292144502053186639397817183561560472
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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More generally, for m integer, exp( Sum_{n>=1} (m^n + y)^n * x^n/n ) is a power series in x and y with integer coefficients.
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FORMULA
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Equals row sums of triangle A155812.
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EXAMPLE
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G.f.: A(x) = 1 + 4*x + 58*x^2 + 7528*x^3 + 11333974*x^4 + 173018964568*x^5 +...
log(A(x)) = 4*x + 10^2*x^2/2 + 28*x^3/3 + 82^4*x^4/4 + 244^5*x^5/5 +...
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PROGRAM
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(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, (3^m+1)^m*x^m/m)+x*O(x^n)), n)}
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CROSSREFS
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Cf. A155203, A155205, A155206, A155812 (triangle), variants: A155201, A155208.
Sequence in context: A099348 A155668 A109056 this_sequence A144992 A037066 A113251
Adjacent sequences: A155201 A155202 A155203 this_sequence A155205 A155206 A155207
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Feb 04 2009
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