cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A002613 Glaisher's function J(n) (18 squares version).

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%I A002613 M5284 N2300 #25 Oct 17 2023 07:17:22
%S A002613 1,44,432,-1136,610,-5568,6048,11456,-3423,26840,-79920,768,-5470,
%T A002613 -77952,263520,61696,73090,-150612,-84240,-692960,-139776,1030080,
%U A002613 -1025568,1410048,-18525,-240680,1355616,10752,-128222,-3396480,-293760
%N A002613 Glaisher's function J(n) (18 squares version).
%C A002613 It would be nice to have a q-series that generates this sequence. Glaisher gives many formulas but they are difficult to follow.
%D A002613 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 A002613 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002613 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002613 Sean A. Irvine, <a href="/A002613/b002613.txt">Table of n, a(n) for n = 1..500</a>
%H A002613 <a href="/index/Ge#Glaisher">Index entries for sequences mentioned by Glaisher</a>
%F A002613 a(n) = -(1/4)*(A002609(2*n) + 16*A002609(n)). - _Sean A. Irvine_, Mar 04 2019
%Y A002613 Cf. A002609.
%K A002613 sign
%O A002613 1,2
%A A002613 _N. J. A. Sloane_
%E A002613 Edited and signs added by _N. J. A. Sloane_, Nov 26 2018
%E A002613 More terms from _Sean A. Irvine_, Mar 04 2019