A002615 Glaisher's function T_1(n).

19, -145, 100, 2191, -8598, 14516, -29080, 114575, -320417, 615666, -1125492, 2139700, -3664750, 5997448, -10103304, 15992719, -23857290, 36059435, -53341900, 75622578, -105762592, 145414140, -198974280, 271923764, -359683403, 468557626

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.

Glaisher table on p. 349 apparently has typos, a(5) = -8592, a(10) = 615566. - Sean A. Irvine, Mar 04 2019

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. 349). [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

Crossrefs

Cf. A002288, A002614.

Formula

a(n) = 19 * A002288(n) - A002614(n). - Sean A. Irvine, Mar 04 2019

Extensions

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

a(5) and a(10) corrected and more terms from Sean A. Irvine, Mar 04 2019