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A156304
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G.f.: A(x) = exp( Sum_{n>=1} sigma(n^3)*x^n/n ), a power series in x with integer coefficients.
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4
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1, 1, 8, 21, 77, 199, 661, 1663, 4852, 12382, 33289, 82877, 213026, 518109, 1279852, 3053404, 7312985, 17093793, 39952528, 91661695, 209709116, 473095589, 1062567288, 2359804486, 5214774263, 11415904502, 24860918943, 53709881911
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OFFSET
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0,3
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COMMENTS
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Compare to g.f. of partition numbers: exp( Sum_{n>=1} sigma(n)*x^n/n ), where sigma(n) = A000203(n) is the sum of the divisors of n.
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LINKS
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FORMULA
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a(n) = (1/n)*Sum_{k=1..n} sigma(k^3) * a(n-k) for n>0, with a(0)=1.
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EXAMPLE
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G.f.: A(x) = 1 + x + 8*x^2 + 21*x^3 + 77*x^4 + 199*x^5 + 661*x^6 +...
log(A(x)) = x + 15*x^2/2 + 40*x^3/3 + 127*x^4/4 + 156*x^5/5 + 600*x^6/6 +...
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PROG
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(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sigma(m^3)*x^m/m)+x*O(x^n)), n)}
(PARI) {a(n)=if(n==0, 1, (1/n)*sum(k=1, n, sigma(k^3)*a(n-k)))}
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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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