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A283580
Expansion of exp( Sum_{n>=1} A283535(n)/n*x^n ) in powers of x.
5
1, 1, 65, 19748, 16799044, 30535636881, 101591759812967, 558649739234980142, 4722932373908389412037, 58154498193439779564557624, 1000058469893323150011227885608, 23226158305362748824532880463596385, 708825166389400019044145225134521489486
OFFSET
0,3
LINKS
FORMULA
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.
a(n) ~ n^(3*n) * (1 + exp(-3)/n^3). - Vaclav Kotesovec, Mar 17 2017
MATHEMATICA
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 *)
PROG
(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)));
for(n=0, 12, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 11 2017
CROSSREFS
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))).
Sequence in context: A120801 A308697 A368890 * A355496 A308491 A349901
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 11 2017
STATUS
approved