A275641 Expansion of (1-q)^k/Product_{j=1..k} (1-q^j) for k=7.

1, -6, 16, -25, 26, -21, 18, -21, 27, -30, 28, -26, 30, -41, 55, -65, 66, -61, 59, -66, 79, -89, 90, -85, 84, -95, 114, -127, 126, -119, 121, -138, 161, -175, 174, -166, 164, -175, 195, -211, 213, -207, 210, -231, 261, -281, 280, -267, 263, -280, 309, -329, 329, -320, 323, -347, 380, -401, 401

Offset: 0

Author

N. J. A. Sloane, Aug 09 2016

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..5000
• A. M. Odlyzko, Differences of the partition function, Acta Arithmetica 49.3 (1988): 237-254.
• Dennis Stanton and Doron Zeilberger, The Odlyzko conjecture and O’Hara’s unimodality proof, Proceedings of the American Mathematical Society 107.1 (1989): 39-42.
• Index entries for linear recurrences with constant coefficients, signature (-6,-20,-49,-98,-169,-259,-359,-455,-531,-573,-573,-531,-455,-359,-259,-169,-98,-49,-20,-6,-1).

Crossrefs

Cf. A275638.

Programs

Mathematica

 CoefficientList[Series[1/((1 + x)^3 (1 - x + x^2) (1 + x^2)(1 + x + x^2)^2 (1 + x + x^2 + x^3 + x^4) (1 + x + x^2 + x^3 + x^4 + x^5 + x^6)), {x, 0, 80}], x] (* Vincenzo Librandi, Feb 04 2017 *)

PARI

Vec(1/((1+x)^3*(1-x+x^2)*(1+x^2)*(1+x+x^2)^2*(1+x+x^2+x^3+x^4)*(1+x+x^2+x^3+x^4+x^5+x^6)) + O(x^100)) \\ Colin Barker, Aug 11 2016

Formula

An equivalent but more complicated g.f.: 1 / ((1+x)^3*(1-x+x^2)*(1+x^2)*(1+x+x^2)^2*(1+x+x^2+x^3+x^4)*(1+x+x^2+x^3+x^4+x^5+x^6)). - Colin Barker, Aug 10 2016