A322031 (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).

1, -8, 18, 16, -111, 72, 178, -144, -126, -232, 384, 432, -301, 240, -1422, -192, 1728, 288, 530, -1424, 162, -888, -1998, 2016, 1633, 1008, 594, 1296, -5568, -1368, 626, -1776, 3204, 632, 10368, -4464, -6686, 2408, -3456, 800, -3231, -2664

Offset

0,2

Comments

This is Glaisher's Q(m).

References

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.

Glaisher, J. W. L. (1906). The arithmetical functions P(m), Q(m), Omega(m). Quart. J. Math, 37, 36-48.

Links

Table of n, a(n) for n=0..41.

J. W. L. Glaisher, On the representations of a number as the sum of two, four, six, eight, ten, and twelve squares, Quart. J. Math. 38 (1907), 1-62 (see p. 5).

Index entries for sequences mentioned by Glaisher

Maple

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;
Q2:=series(Q1, q, 1000); Q3 := seriestolist(Q2);
Q4:=[seq(Q3[8*i+5], i=0..120)];

Crossrefs

Sequence in context: A133202 A217424 A332969 * A196207 A196474 A251258

Adjacent sequences: A322028 A322029 A322030 * A322032 A322033 A322034

Keyword

sign,changed

Author

N. J. A. Sloane, Nov 24 2018

Status

approved