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Absolute value of Glaisher's beta'(2n+1).
(Formerly M3205 N1297)
2

%I M3205 N1297 #19 Oct 14 2023 23:52:54

%S 0,1,4,2,8,13,28,26,56,69,48,134,80,182,84,312,280,204,332,142,816,91,

%T 196,780,224,526,244,1198,2216,767,508,390,400,1167,1424,466,2264,

%U 1391,1392,3796,1480,11,1768,2274,1320,1508,1984,8450

%N Absolute value of Glaisher's beta'(2n+1).

%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 J. W. L. Glaisher, <a href="https://books.google.com/books?id=bLs9AQAAMAAJ&amp;pg=RA1-PA1">On the representations of a number as the sum of two, four, six, eight, ten, and twelve squares</a>, Quart. J. Math. 38 (1907), 1-62 (see p. 56).

%H <a href="/index/Ge#Glaisher">Index entries for sequences mentioned by Glaisher</a>

%t Abs[CoefficientList[Series[x*QPochhammer[x]^4*QPochhammer[x^4]^8, {x, 0, 60}], x]] (* _Vaclav Kotesovec_, Oct 08 2019 *)

%Y For beta' itself, see A225872, and for beta, see A322032.

%K nonn

%O 0,3

%A _N. J. A. Sloane_