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%I M2722 N1090 #36 Dec 06 2023 08:34:16
%S 1,3,8,16,30,46,64,96,126,158,216,256,302,396,448,512,636,702,792,960,
%T 1052,1118,1344,1472,1550,1866,1944,2048,2442,2540,2688,3072,3212,
%U 3388,3888,4032,4094,4746,4928,5056,5832,5852,5976,6912,7020,7180,8064,8192
%N Generalized class numbers c_(n,1).
%C Let L_a(s) = Sum_{k>=0} (-a|2k+1) /(2k+1)^s be a Dirichlet series, where (-a|2k+1) is the Jacobi symbol. Then the c_(a,n) are defined by L_a(2n+1) = (Pi/(2a))^(2n+1)*sqrt(a)*c_(a,n)/(2n)! for n=0,1,2,..., a=1,2,3,...
%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 D. Shanks, <a href="http://dx.doi.org/10.1090/S0025-5718-1967-0223295-5">Generalized Euler and class numbers</a>. Math. Comp. 21 (1967) 689-694.
%H D. Shanks, <a href="http://dx.doi.org/10.1090/S0025-5718-68-99652-X">Corrigendum: Generalized Euler and class numbers</a>. Math. Comp. 22, (1968) 699.
%H D. Shanks, <a href="/A000003/a000003.pdf">Generalized Euler and class numbers</a>, Math. Comp. 21 (1967), 689-694; 22 (1968), 699. [Annotated scanned copy]
%t amax = 50; nmax = 1; km0 = 10; Clear[cc]; L[a_, s_, km_] := Sum[ JacobiSymbol[-a, 2 k + 1]/(2 k + 1)^s, {k, 0, km}]; c[1, n_, km_] := 2 (2 n)! L[1, 2 n + 1, km] (2/Pi)^(2 n + 1) // Round; c[a_ /; a > 1, n_, km_] := (2 n)! L[a, 2 n + 1, km] (2 a/Pi)^(2 n + 1)/Sqrt[a] // Round; cc[km_] := cc[km] = Table[c[a, n, km], {a, 1, amax}, {n, 0, nmax}]; cc[km0]; cc[ km = 2 km0]; While[cc[km] != cc[km/2, km = 2 km]]; A000233 = cc[km][[All, 2]] (* _Jean-François Alcover_, Feb 06 2016 *)
%Y Cf. A000508, A000362.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
%E More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 02 2000
%E Name clarified by _James C. McMahon_, Nov 30 2023
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