A283336 Expansion of exp( Sum_{n>=1} -sigma_6(n)*x^n/n ) in powers of x.

1, -1, -32, -211, -285, 5179, 44784, 162062, -125122, -5187417, -32587255, -95706881, 122837972, 3039216222, 17745876032, 52825817007, -24340390929, -1256623249600, -7805634068163, -26364952524572, -20649978457115, 368666542515083, 2777231006764690

Offset: 0

Author

Seiichi Manyama, Mar 05 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=5 of A283272.

Cf. A023874 (exp( Sum_{n>=1} sigma_6(n)*x^n/n )).

Cf. exp( Sum_{n>=1} -sigma_k(n)*x^n/n ): A010815 (k=1), A073592 (k=2), A283263 (k=3), A283264 (k=4), A283271 (k=5), this sequence (k=6), A283337 (k=7), A283338 (k=8), A283339 (k=9), A283340 (k=10).

Programs

Mathematica

a[n_] := If[n<1, 1,-(1/n) * Sum[DivisorSigma[6, k] a[n - k], {k, n}]]; Table[a[n], {n, 0, 22}] (* Indranil Ghosh, Mar 16 2017 *)

PARI

a(n) = if(n<1, 1, -(1/n) * sum(k=1, n, sigma(k, 6) * a(n - k)));
for(n=0, 22, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 16 2017

Formula

G.f.: Product_{n>=1} (1 - x^n)^(n^5).

a(n) = -(1/n)*Sum_{k=1..n} sigma_6(k)*a(n-k).