A002290 Absolute value of Glaisher's alpha(n). (Formerly M3403 N1376)

1, 4, 10, 56, 29, 332, 30, 1064, 302, 1940, 288, 1960, 1071, 1192, 1938, 736, 2000, 1488, 5014, 7288, 4170, 10644, 8482, 11184, 12647, 15544, 15590, 9992, 25424, 4604, 26610, 2472, 28972, 3140, 26464, 39416, 31338, 24764, 25248, 16176, 48871, 67540, 60364, 29256, 50874, 12656

Offset

0,2

Comments

In Glaisher (1907) alpha(m) is defined in section 63 on page 37. This is A225543 with signs omitted. - Michael Somos, Apr 24 2014

References

J. W. L. Glaisher, On the representation of a number as sum of 2, 4, 6, 8, 10, and 12 squares, Quart. J. Pure and Appl. Math. 38 (1907), 1-62 (see p. 56).

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

Table of n, a(n) for n=0..45.

Formula

a(n) = |A225543(n)|. - Michael Somos, May 17 2013

Mathematica

QP = QPochhammer; s = (QP[q^2]^6/(QP[q]*QP[q^4]^2))^4 + O[q]^50; Abs[ CoefficientList[s, q]] (* Jean-François Alcover, Nov 30 2015, adapted from PARI *)

Prog

(PARI)
N = 66;  q = 'q + O('q^N);
sgf = (eta(q^2)^6/(eta(q)*eta(q^4)^2))^4
v = abs( Vec(sgf) )
\\ Joerg Arndt, May 17 2013

Crossrefs

Cf. A225543.

Sequence in context: A013589 A367430 A225543 * A336997 A222569 A348514

Adjacent sequences: A002287 A002288 A002289 * A002291 A002292 A002293

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Joerg Arndt, May 17 2013

Status

approved