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A072836 Exponents occurring in expansion of F_10(q^2). 3

%I

%S 0,9,16,20,21,24,25,29,36,40,41,44,45,49,56,60,61,64,65,69,76,80,81,

%T 84,85,89,96,100,101,104,105,109,116,120,121,124,125,129,136,140,141,

%U 144,145,149,156,160,161,164,165,169,176,180,181,184,185,189,196,200,201,204,205,209,216

%N Exponents occurring in expansion of F_10(q^2).

%C Nonnegative numbers congruent to {0, 1, 4, 5, 9, 16} (mod 20), except for {1, 4, 5}. Also, norms of vectors in the A*_9 lattice. - _Andrey Zabolotskiy_, Nov 10 2021

%H G. C. Greubel, <a href="/A072836/b072836.txt">Table of n, a(n) for n = 0..1000</a>

%H S. Ahlgren, <a href="https://doi.org/10.1090/S0002-9939-99-05181-3">The sixth, eighth, ninth and tenth powers of Ramanujan's theta function</a>, Proc. Amer. Math. Soc. 128 (2000), 1333-1338

%F G.f.: -x*(5*x^6-x^5-3*x^4-x^3-4*x^2-7*x-9) / (x^7-x^6-x+1). - _Colin Barker_, Jul 31 2013

%t f[x_, y_]:= QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; F[10,q_]:= f[q^5, q^5]^10/f[q, q] - 8*q^2*f[q^5, q^5]^5* QPochhammer[q^10]^5/QPochhammer[q^2] - (27*q^4*f[q^5, q^5]^5 - 125*q^9*f[q^5, q^5]*f[q^10, q^30]^4 + 5*q^5*f[q^5, q^5]*f[q^2, q^6]^4)* QPochhammer[q^20]^5/QPochhammer[q^4] - 17*q^5*f[q, q]*f[q^5, q^15]^8 + 2*q*f[q, q]*f[q^5, q^5]^4*f[q^2, q^6]^4 - 20*q^8*f[q, q]*QPochhammer[q^20]^10/QPochhammer[q^4]^2 + 5*q^4*f[q, q]*QPochhammer[q^10]^10/QPochhammer[q^2]^2; cfs = CoefficientList[Series[F[10, q], {q, 0, 500}], q]; Take[Pick[Range[Length[cfs]] - 1, Sign[Abs[cfs]], 1], 50] (* _G. C. Greubel_, Apr 16 2018 *)

%Y Cf. A023921.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jul 25 2002

%E Terms a(27) onward added by _G. C. Greubel_, Apr 16 2018

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Last modified December 5 12:24 EST 2021. Contains 349557 sequences. (Running on oeis4.)