A283369 -id:A283369 - cp's OEIS frontend

A283510 Expansion of exp( Sum_{n>=1} A283369(n)/n*x^n ) in powers of x.

1, 1, 257, 531698, 4295531890, 95371863221411, 4738477950914329100, 459991301719292572342573, 79228623778497392212453912974, 22528478894247280128054776211273960, 10000022549030658394108744658459680045250

Offset: 0

Seiichi Manyama, Mar 17 2017

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..120

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))).

CoefficientList[Series[Product[1/(1 - x^k)^(k^(4k)), {k, 1, 10}], {x, 0, 10}], x] (* Indranil Ghosh, Mar 17 2017 *)

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

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

A283803 Expansion of exp( Sum_{n>=1} -A283369(n)/n*x^n ) in powers of x.

Original entry on oeis.org

1, -1, -256, -531185, -4294403215, -95363000657073, -4738284730302658391, -459981771468075494207385, -79227701254823507875355278590, -22528320196093613328344381426130010, -9999977451048811940735941180766259658078

Offset: 0

Seiichi Manyama, Mar 17 2017

sign

Seiichi Manyama, Table of n, a(n) for n = 0..120

Cf. Product_{k>=1} (1 - x^k)^(k^(m*k)): A010815 (m=0), A283499 (m=1), A283534 (m=2), A283536 (m=3), this sequence (m=4).

Cf. A283510 (Product_{k>=1} 1/(1 - x^k)^(k^(4*k))).

CoefficientList[Series[Product[(1 - x^k)^(k^(4k)), {k, 1, 10}], {x, 0, 10}], x] (* Indranil Ghosh, Mar 17 2017 *)

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

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

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

cp's OEIS Frontend

A283510 Expansion of exp( Sum_{n>=1} A283369(n)/n*x^n ) in powers of x.

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