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A155206
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G.f.: A(x) = exp( Sum_{n>=1} (3^n - 1)^n/2^(n-1) * x^n/n ), a power series in x with integer coefficients.
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4
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1, 2, 18, 1498, 1283090, 10377556482, 775351592888722, 532444511048570910746, 3349121447720205394546014978, 192371436319107536207473420480152034, 100642626897912335112447860229547933463000450
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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 - 1)^n/(m-1)^(n-1) * x^n/n ) is a power series in x with integer coefficients.
Note that g.f. exp( Sum_{n>=1} (3^n - 1)^n/2^n * x^n/n ) has fractional coefficients as a power series in x.
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LINKS
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EXAMPLE
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G.f.: A(x) = 1 + 2*x + 18*x^2 + 1498*x^3 + 1283090*x^4 + 10377556482*x^5 +...
log(A(x)) = 2*x + 8^2/2*x^2/2 + 26^3/2^2*x^3/3 + 80^4/2^3*x^4/4 + 242^5/2^4*x^5/5 +...
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PROG
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(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, (3^m-1)^m/2^(m-1)*x^m/m)+x*O(x^n)), n)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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