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Glaisher's function J(n) (18 squares version).
(Formerly M5284 N2300)
1

%I M5284 N2300 #25 Oct 17 2023 07:17:22

%S 1,44,432,-1136,610,-5568,6048,11456,-3423,26840,-79920,768,-5470,

%T -77952,263520,61696,73090,-150612,-84240,-692960,-139776,1030080,

%U -1025568,1410048,-18525,-240680,1355616,10752,-128222,-3396480,-293760

%N Glaisher's function J(n) (18 squares version).

%C It would be nice to have a q-series that generates this sequence. Glaisher gives many formulas but they are difficult to follow.

%D J. W. L. Glaisher, On the representation of a number as sum of 18 squares, Quart. J. Math. 38 (1907), 289-351 (see p. 329). [The whole 1907 volume of The Quarterly Journal of Pure and Applied Mathematics, volume 38, is freely available from Google Books]

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Sean A. Irvine, <a href="/A002613/b002613.txt">Table of n, a(n) for n = 1..500</a>

%H <a href="/index/Ge#Glaisher">Index entries for sequences mentioned by Glaisher</a>

%F a(n) = -(1/4)*(A002609(2*n) + 16*A002609(n)). - _Sean A. Irvine_, Mar 04 2019

%Y Cf. A002609.

%K sign

%O 1,2

%A _N. J. A. Sloane_

%E Edited and signs added by _N. J. A. Sloane_, Nov 26 2018

%E More terms from _Sean A. Irvine_, Mar 04 2019