A283163 Expansion of exp( Sum_{n>=1} -sigma(4*n)*x^n/n ) in powers of x.

1, -7, 17, -14, 2, -21, 36, 13, -26, -24, 10, 12, -17, 34, 22, 19, -96, -10, 14, 38, 0, 12, -23, 72, -38, -2, -11, -64, -34, 0, 72, 84, -26, 0, 0, -79, 60, 24, -32, -58, -7, -84, 50, 26, 120, 0, 0, 46, -34, -64, 10, -119, 70, 0, 22, -70, 36, 37, -120, 0

Offset

0,2

Links

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

Formula

G.f.: Product_{n>=1} (1 - x^n)^7/(1 - x^(2*n))^3.

a(n) = -(1/n)*Sum_{k=1..n} sigma(4*k)*a(n-k). - Seiichi Manyama, Mar 04 2017

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/4) * exp(Pi / 24) * Pi * 2^(7/8) / Gamma(3/4)^4 = A389017. - Simon Plouffe, Sep 22 2025

Crossrefs

Cf. A182820 (exp( Sum_{n>=1} sigma(4*n)*x^n/n )), A193553 (sigma(4*n)).

Cf. exp( Sum_{n>=1} -sigma(k*n)*x^n/n ): A115110 (k=2), A185654 (k=3), this sequence (k=4), A282937 (k=5), A283164 (k=6), A282942 (k=7), A283168 (k=8), A283169 (k=9).

Sequence in context: A393234 A274916 A128713 * A196164 A071615 A067459

Adjacent sequences: A283160 A283161 A283162 * A283164 A283165 A283166

Keyword

sign

Author

Seiichi Manyama, Mar 02 2017

Status

approved