A283168 Expansion of exp( Sum_{n>=1} -sigma(8*n)*x^n/n ) in powers of x.

1, -15, 97, -350, 770, -1133, 1540, -2731, 4230, -3960, 3402, -6580, 9167, -5390, 4310, -11061, 12320, -5306, 2030, -7530, 14784, -4340, -10119, -9240, 20090, 11438, -17275, -4928, 2270, 14080, -26840, 7700, 16646, 24640, -53760, 7449, 10780, 46200, -61600

Offset

0,2

Links

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

Formula

G.f.: Product_{n>=1} (1 - x^n)^15/(1 - x^(2*n))^7.

a(n) = -(1/n)*Sum_{k=1..n} sigma(8*k)*a(n-k). - Seiichi Manyama, Mar 04 2017

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/8) * exp(Pi / 24) * Pi^2*2^(7/8) / Gamma(3/4)^8 = A389018. - Simon Plouffe, Sep 22 2025

Crossrefs

Cf. A283120 (exp( Sum_{n>=1} sigma(8*n)*x^n/n )), A283122 (sigma(8*n)).

Cf. exp( Sum_{n>=1} -sigma(k*n)*x^n/n ): A115110 (k=2), A185654 (k=3), A283163 (k=4), A282937 (k=5), A283164 (k=6), A282942 (k=7), this sequence (k=8), A283169 (k=9).

Sequence in context: A289705 A296538 A298105 * A232296 A278203 A159528

Adjacent sequences: A283165 A283166 A283167 * A283169 A283170 A283171

Keyword

sign

Author

Seiichi Manyama, Mar 02 2017

Status

approved