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A275641 Expansion of (1-q)^k/Product_{j=1..k} (1-q^j) for k=7. 3

%I

%S 1,-6,16,-25,26,-21,18,-21,27,-30,28,-26,30,-41,55,-65,66,-61,59,-66,

%T 79,-89,90,-85,84,-95,114,-127,126,-119,121,-138,161,-175,174,-166,

%U 164,-175,195,-211,213,-207,210,-231,261,-281,280,-267,263,-280,309,-329,329,-320,323,-347,380,-401,401

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

%H Vincenzo Librandi, <a href="/A275641/b275641.txt">Table of n, a(n) for n = 0..5000</a>

%H A. M. Odlyzko, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa49/aa4932.pdf">Differences of the partition function</a>, Acta Arithmetica 49.3 (1988): 237-254.

%H Dennis Stanton and Doron Zeilberger, <a href="https://doi.org/10.1090/S0002-9939-1989-0972238-1">The Odlyzko conjecture and O’Hara’s unimodality proof</a>, Proceedings of the American Mathematical Society 107.1 (1989): 39-42.

%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (-6,-20,-49,-98,-169,-259,-359,-455,-531,-573,-573,-531,-455,-359,-259,-169,-98,-49,-20,-6,-1).

%F 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

%t 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 *)

%o (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

%Y Cf. A275638.

%K sign,easy

%O 0,2

%A _N. J. A. Sloane_, Aug 09 2016

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Last modified June 21 06:55 EDT 2021. Contains 345358 sequences. (Running on oeis4.)