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A283580
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Expansion of exp( Sum_{n>=1} A283535(n)/n*x^n ) in powers of x.
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5
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1, 1, 65, 19748, 16799044, 30535636881, 101591759812967, 558649739234980142, 4722932373908389412037, 58154498193439779564557624, 1000058469893323150011227885608, 23226158305362748824532880463596385, 708825166389400019044145225134521489486
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: Product_{k>=1} 1/(1 - x^k)^(k^(3*k)).
a(n) = (1/n)*Sum_{k=1..n} A283535(k)*a(n-k) for n > 0.
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MATHEMATICA
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A[n_] := Sum[d^(3*d + 1), {d, Divisors[n]}]; a[n_] := If[n==0, 1, (1/n)*Sum[A[k]*a[n - k], {k, n}]]; Table[a[n], {n, 0, 12}] (* Indranil Ghosh, Mar 11 2017 *)
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PROG
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(PARI) A(n) = sumdiv(n, d, d^(3*d + 1));
a(n) = if(n==0, 1, (1/n)*sum(k=1, n, A(k)*a(n - k)));
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CROSSREFS
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Cf. Product_{k>=1} 1/(1 - x^k)^(k^(m*k)): A000041 (m=0), A023880 (m=1), A283579 (m=2), this sequence (m=3).
Cf. A283536 (Product_{k>=1} (1 - x^k)^(k^(3*k))).
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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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