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Glaisher's function theta(n) (18 squares version).
(Formerly M4459 N1890)
2

%I M4459 N1890 #23 Oct 17 2023 07:19:41

%S 0,-7,128,-975,4608,-16340,48384,-124303,281600,-583746,1146240,

%T -2125108,3691008,-6151880,10055424,-15914895,24136704,-35748899,

%U 52583040,-75877938,105994240,-145580124,200279808,-272040500,359036928,-468767690,615599360

%N Glaisher's function theta(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. 349). [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="/A002614/b002614.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) = (A321546(n) - A002288(n)) / 17. - _Sean A. Irvine_, Mar 04 2019

%Y Cf. A002288, A321546.

%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