A275639 Expansion of (1-q)^k/Product_{j=1..k} (1-q^j) for k=5.

1, -4, 7, -7, 5, -4, 4, -4, 5, -7, 8, -8, 9, -11, 12, -11, 9, -8, 9, -11, 13, -15, 16, -15, 14, -15, 16, -15, 14, -15, 17, -19, 21, -22, 21, -19, 18, -19, 21, -22, 22, -23, 25, -26, 26, -26, 25, -23, 23, -26, 29, -30, 30, -30, 30, -30, 30, -30, 30, -30, 31, -34, 37, -37, 35, -34, 34, -34, 35

Offset: 0

Author

N. J. A. Sloane, Aug 09 2016

Keywords

• sign
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• 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 (-4,-9,-15,-20,-22,-20,-15,-9,-4,-1)

Crossrefs

Cf. A275638.

Programs

PARI

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

Formula

Equivalent g.f.: 1 / ((1+x)^2*(1+x^2)*(1+x+x^2)*(1+x+x^2+x^3+x^4)). - Colin Barker, Aug 10 2016

a(n) = -4*a(n-1) - 9*a(n-2) - 15*a(n-3) - 20*a(n-4) - 22*a(n-5) - 20*a(n-6) - 15*a(n-7) - 9*a(n-8) - 4*a(n-9) - a(n-10). - Ilya Gutkovskiy, Aug 10 2016