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Glaisher's function V(n).
(Formerly M3235 N1305)
2

%I M3235 N1305 #20 Mar 04 2019 01:53:55

%S 0,1,4,-4,-32,-16,56,80,192,98,-740,-704,96,-224,2440,3520,-2624,-351,

%T -780,-10632,2688,2960,-9496,18176,14208,-3934,12552,-9856,-24608,

%U -9760,-2720,-25344,-35520,31106,34160,62844,84576,3120,-21880,-82272,27520,-96768,-237316,130240,-92832,37984,305296,-183296,37632,208803

%N Glaisher's function V(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. 320). [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 <a href="/index/Ge#Glaisher">Index entries for sequences mentioned by Glaisher</a>

%F a(n) = Sum_{k=1..floor(n/2)} A004018(n - 2*k) * A002288(k). - _Sean A. Irvine_, Mar 04 2019

%Y Cf. A002288, A004018.

%K sign

%O 1,3

%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