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%I #17 Dec 15 2024 07:22:16
%S 1,-8,18,16,-111,72,178,-144,-126,-232,384,432,-301,240,-1422,-192,
%T 1728,288,530,-1424,162,-888,-1998,2016,1633,1008,594,1296,-5568,
%U -1368,626,-1776,3204,632,10368,-4464,-6686,2408,-3456,800,-3231,-2664
%N (Sum_{t=0..oo} ((-1)^t*(2*t+1)*q^((2*t+1)^2)))^3 * (Sum_{t=0..oo} q^((2*t+1)^2)) = Sum_{k=0..oo} a(k)*q^(8*k+4).
%C This is Glaisher's Q(m).
%D J. W. L. Glaisher, On the representations of a number as a sum of four squares, and on some allied arithmetical functions, Quarterly Journal of Pure and Applied Mathematics, 36 (1905), 305-358. See p. 340.
%D Glaisher, J. W. L. (1906). The arithmetical functions P(m), Q(m), Omega(m). Quart. J. Math, 37, 36-48.
%H J. W. L. Glaisher, <a href="https://books.google.com/books?id=bLs9AQAAMAAJ&pg=RA1-PA1">On the representations of a number as the sum of two, four, six, eight, ten, and twelve squares</a>, Quart. J. Math. 38 (1907), 1-62 (see p. 5).
%H <a href="/index/Ge#Glaisher">Index entries for sequences mentioned by Glaisher</a>
%p Q1:= (add( (-1)^t*(2*t+1)*q^((2*t+1)^2),t=0..1001))^3 * (add(q^((2*t+1)^2),t=0..1001))^1;
%p Q2:=series(Q1,q,1000); Q3 := seriestolist(Q2);
%p Q4:=[seq(Q3[8*i+5],i=0..120)];
%K sign
%O 0,2
%A _N. J. A. Sloane_, Nov 24 2018