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Absolute value of Glaisher's alpha(n).
(Formerly M3403 N1376)
1

%I M3403 N1376 #37 Oct 14 2023 23:52:18

%S 1,4,10,56,29,332,30,1064,302,1940,288,1960,1071,1192,1938,736,2000,

%T 1488,5014,7288,4170,10644,8482,11184,12647,15544,15590,9992,25424,

%U 4604,26610,2472,28972,3140,26464,39416,31338,24764,25248,16176,48871,67540,60364,29256,50874,12656

%N Absolute value of Glaisher's alpha(n).

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

%D 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).

%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).

%F a(n) = |A225543(n)|. - _Michael Somos_, May 17 2013

%t 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 *)

%o (PARI)

%o N = 66; q = 'q + O('q^N);

%o sgf = (eta(q^2)^6/(eta(q)*eta(q^4)^2))^4

%o v = abs( Vec(sgf) )

%o \\ _Joerg Arndt_, May 17 2013

%Y Cf. A225543.

%K nonn

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Joerg Arndt_, May 17 2013