A002612 Glaisher's function U(n).

1, 12, 48, 16, -414, -960, 672, 4800, 2721, -9064, -8880, 6912, -2398, -13440, 29280, 30976, -10878, 57228, -9360, -252384, -53760, 177600, -113952, 107520, 436131, -16488, 150624, 96768, -915678, -585600, -32640, 248832, 710400, -466408

Offset: 1

Author

N. J. A. Sloane

Keywords

• sign

Comments

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

References

• 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]
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..500
• Index entries for sequences mentioned by Glaisher

Formula

a(n) = A002609(n) + 32*A002611(n). - Sean A. Irvine, Mar 04 2019

Extensions

Edited and signs added by N. J. A. Sloane, Nov 26 2018

More terms from Sean A. Irvine, Mar 04 2019