A275640 Expansion of (1-q)^k/Product_{j=1..k} (1-q^j) for k=6.

1, -5, 11, -14, 12, -9, 9, -13, 20, -26, 27, -25, 26, -33, 43, -49, 47, -42, 43, -53, 67, -77, 78, -73, 72, -82, 98, -108, 107, -102, 104, -118, 138, -151, 150, -142, 141, -155, 178, -194, 194, -187, 189, -206, 230, -246, 245, -235, 235, -255, 285, -305, 305, -295, 295, -315, 345, -365, 365

Offset

0,2

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 (-5,-14,-29,-49,-71,-90,-101,-101,-90,-71,-49,-29,-14,-5,-1).

Formula

Equivalent 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)). - Colin Barker, Aug 10 2016

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)), {x, 0, 100}], x] (* or *) LinearRecurrence[{-5, -14, -29, -49, -71, -90, -101, -101, -90, -71, -49, -29, -14, -5, -1}, {1, -5, 11, -14, 12, -9, 9, -13, 20, -26, 27, -25, 26, -33, 43}, 100] (* Harvey P. Dale, Mar 14 2023 *)

Crossrefs

Cf. A275638.

Sequence in context: A073615 A346147 A275118 * A275805 A340605 A313993

Adjacent sequences: A275637 A275638 A275639 * A275641 A275642 A275643

Keyword

sign,easy

Author

N. J. A. Sloane, Aug 09 2016

Status

approved