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A283536 Expansion of exp( Sum_{n>=1} -A283535(n)/n*x^n ) in powers of x. 5
1, -1, -64, -19619, -16755517, -30499543213, -101528172949440, -558442022082754554, -4721800698082895269442, -58144976385942395405449505, -999941534906642496357956893139, -23224150593200781968944997552887957, -708778584588517237886357058373629079824 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..152

FORMULA

G.f.: Product_{k>=1} (1 - x^k)^(k^(3*k)).

a(n) = -(1/n)*Sum_{k=1..n} A283535(k)*a(n-k) for n > 0.

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 - x^k)^(k^(m*k)): A010815 (m=0), A283499 (m=1), A283534 (m=2), this sequence (m=3).

Cf. A283580 (Product_{k>=1} 1/(1 - x^k)^(k^(3*k))).

Sequence in context: A013781 A187407 A271241 * A089208 A083282 A082502

Adjacent sequences:  A283533 A283534 A283535 * A283537 A283538 A283539

KEYWORD

sign

AUTHOR

Seiichi Manyama, Mar 10 2017

STATUS

approved

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Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)