A283510 - OEIS

%I #28 Mar 17 2017 11:10:52

%S 1,1,257,531698,4295531890,95371863221411,4738477950914329100,

%T 459991301719292572342573,79228623778497392212453912974,

%U 22528478894247280128054776211273960,10000022549030658394108744658459680045250

%N Expansion of exp( Sum_{n>=1} A283369(n)/n*x^n ) in powers of x.

%H Seiichi Manyama, <a href="/A283510/b283510.txt">Table of n, a(n) for n = 0..120</a>

%F G.f.: Product_{k>=1} 1/(1 - x^k)^(k^(4*k)).

%F a(n) = (1/n)*Sum_{k=1..n} A283369(k)*a(n-k) for n > 0.

%F a(n) ~ n^(4*n) * (1 + exp(-4)/n^4). - _Vaclav Kotesovec_, Mar 17 2017

%t CoefficientList[Series[Product[1/(1 - x^k)^(k^(4k)), {k, 1, 10}], {x, 0, 10}], x] (* _Indranil Ghosh_, Mar 17 2017 *)

%o (PARI) A(n) = sumdiv(n, d, d^(4*d + 1));

%o a(n) = if(n<1, 1, (1/n) * sum(k=1, n, A(k) * a(n - k)));

%o for(n=0, 10, print1(a(n),", ")) \\ _Indranil Ghosh_, Mar 17 2017

%Y 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).

%Y Cf. A283803 (Product_{k>=1} (1 - x^k)^(k^(4*k))).

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 17 2017