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Glaisher's function U(n).
(Formerly M4836 N2067)
1

%I M4836 N2067 #23 Oct 17 2023 07:18:10

%S 1,12,48,16,-414,-960,672,4800,2721,-9064,-8880,6912,-2398,-13440,

%T 29280,30976,-10878,57228,-9360,-252384,-53760,177600,-113952,107520,

%U 436131,-16488,150624,96768,-915678,-585600,-32640,248832,710400,-466408

%N Glaisher's function U(n).

%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. 325). [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="/A002612/b002612.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) = A002609(n) + 32*A002611(n). - _Sean A. Irvine_, Mar 04 2019

%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