A283164 Expansion of exp( Sum_{n>=1} -sigma(6*n)*x^n/n ) in powers of x.

1, -12, 58, -133, 95, 194, -418, 97, 325, -99, -238, 169, -217, 131, 190, -145, 441, -647, 169, -527, 72, 1129, 313, -972, 2, -491, -565, 1944, -1175, -216, 972, 863, -1259, 288, 0, -1155, -1355, -207, 2925, 1753, 1402, -2387, -2257, -1030, 315, 432, -72, 1621, 358

Offset

0,2

Links

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

Formula

G.f.: Product_{n>=1} (1 - x^n)^12 * (1 - x^(6*n))/((1 - x^(2*n))^4 * (1 - x^(3*n))^3).

a(n) = -(1/n)*Sum_{k=1..n} sigma(6*k)*a(n-k). - Seiichi Manyama, Mar 04 2017

Crossrefs

Cf. A224613 (sigma(6*n)), A283119 (exp( Sum_{n>=1} sigma(6*n)*x^n/n )).

Cf. exp( Sum_{n>=1} -sigma(k*n)*x^n/n ): A115110 (k=2), A185654 (k=3), A283163 (k=4), A282937 (k=5), this sequence (k=6), A282942 (k=7), A283168 (k=8), A283169 (k=9).

Sequence in context: A190297 A072259 A272233 * A242983 A167533 A244907

Adjacent sequences: A283161 A283162 A283163 * A283165 A283166 A283167

Keyword

sign

Author

Seiichi Manyama, Mar 02 2017

Status

approved