A022667 Expansion of Product_{m>=1} (1 - m*q^m)^7.

1, -7, 7, 42, -56, -105, -126, 489, 987, -651, -833, -6062, -3101, 10381, 21040, 34720, -20692, -46732, -173642, -238014, 25193, 614802, 1161951, 982667, 981253, -3028025, -5721548, -10660692, -7448428, 4778767, 21412363, 79760653, 64512273, 37376857, -64640856, -220678215

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

G.f.: exp(-7*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018

Mathematica

With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^7, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Feb 24 2018 *)

Prog

(PARI) m=50; q='q+O('q^m); Vec(prod(n=1, m, (1-n*q^n)^7)) \\ G. C. Greubel, Feb 24 2018
(Magma) Coefficients(&*[(1-m*x^m)^7:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 24 2018

Crossrefs

Column k=7 of A297323.

Sequence in context: A153721 A286985 A151791 * A143430 A219399 A219447

Adjacent sequences: A022664 A022665 A022666 * A022668 A022669 A022670

Keyword

sign

Author

N. J. A. Sloane

Extensions

Terms a(31) onward added by G. C. Greubel, Feb 24 2018

Status

approved