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A155210
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G.f.: A(x) = exp( Sum_{n>=1} (4^n - 1)^n/3^(n-1) * x^n/n ), a power series in x with integer coefficients.
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4
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1, 3, 42, 9378, 39179127, 2766569881269, 3234201150559172040, 62076685218110095082936700, 19446778350632942283719042004313725, 98999235365955012033013202024947235500115415
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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} (4^n - 1)^n/3^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 + 3*x + 42*x^2 + 9378*x^3 + 39179127*x^4 +...
log(A(x)) = 3*x + 15^2/3*x^2/2 + 63^3/3^2*x^3/3 + 255^4/3^3*x^4/4 +...
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PROG
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(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, (4^m-1)^m/3^(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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