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A283510
Expansion of exp( Sum_{n>=1} A283369(n)/n*x^n ) in powers of x.
3
1, 1, 257, 531698, 4295531890, 95371863221411, 4738477950914329100, 459991301719292572342573, 79228623778497392212453912974, 22528478894247280128054776211273960, 10000022549030658394108744658459680045250
OFFSET
0,3
LINKS
FORMULA
G.f.: Product_{k>=1} 1/(1 - x^k)^(k^(4*k)).
a(n) = (1/n)*Sum_{k=1..n} A283369(k)*a(n-k) for n > 0.
a(n) ~ n^(4*n) * (1 + exp(-4)/n^4). - Vaclav Kotesovec, Mar 17 2017
MATHEMATICA
CoefficientList[Series[Product[1/(1 - x^k)^(k^(4k)), {k, 1, 10}], {x, 0, 10}], x] (* Indranil Ghosh, Mar 17 2017 *)
PROG
(PARI) A(n) = sumdiv(n, d, d^(4*d + 1));
a(n) = if(n<1, 1, (1/n) * sum(k=1, n, A(k) * a(n - k)));
for(n=0, 10, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 17 2017
CROSSREFS
Cf. Product_{k>=1} 1/(1 - x^k)^(k^(m*k)): A000041 (m=0), A023880 (m=1), A283579 (m=2), A283580 (m=3), this sequence (m=4).
Cf. A283803 (Product_{k>=1} (1 - x^k)^(k^(4*k))).
Sequence in context: A351865 A218723 A097736 * A103349 A291506 A275098
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 17 2017
STATUS
approved