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
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).
Crossrefs
Cf. A275638.
Programs
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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 *)
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