A283243 Expansion of exp( Sum_{n>=1} -sigma_2(3*n)*x^n/n ) in powers of x.

1, -10, 25, 53, -270, -77, 1057, 610, -2031, -5438, -1953, 17236, 34121, 3351, -103369, -195850, -55471, 468448, 1067785, 764094, -1430780, -4974559, -6242563, 334620, 16946199, 34459888, 29243953, -24503978, -124514921, -205795663, -140256312, 191109263

Offset

0,2

Links

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

Formula

a(n) = -(1/n)*Sum_{k=1..n} sigma_2(3*k)*a(n-k). - Seiichi Manyama, Mar 04 2017

Prog

(PARI) A283243_vec(m)=Vec(exp(sum(n=1, m, -sigma(3*n, 2)*x^n/n)+x*O(x^m))) \\ Yields m+1 terms a(0..m). - M. F. Hasler, Mar 05 2017

Crossrefs

Cf. A283237 (sigma_2(3*n)), A283238 (exp( Sum_{n>=1} sigma_2(3*n)*x^n/n )).

Cf. exp( Sum_{n>=1} -sigma_k(3*n)*x^n/n ): A185654 (k=1), this sequence (k=2).

Cf. exp( Sum_{n>=1} -sigma_2(m*n)*x^n/n ): A073592 (m=1), A283242 (m=2), this sequence (m=3).

Sequence in context: A020179 A022670 A072277 * A263310 A063424 A137930

Adjacent sequences: A283240 A283241 A283242 * A283244 A283245 A283246

Keyword

sign

Author

Seiichi Manyama, Mar 03 2017

Status

approved