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 A000362 Generalized class numbers c_(n,2). (Formerly M4016 N1664) 5
 5, 57, 352, 1280, 3522, 7970, 15872, 29184, 49410, 79042, 122400, 180224, 257314, 362340, 492032, 655360, 867588, 1117314, 1420320, 1803264, 2237380, 2745154, 3380736, 4080640, 4881250, 5874150, 6928416, 8126464, 9600870, 11133604 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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,... REFERENCES 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=1..30. D. Shanks, Generalized Euler and class numbers. Math. Comp. 21 (1967) 689-694. D. Shanks, Corrigenda to: "Generalized Euler and class numbers", Math. Comp. 22 (1968), 699 D. Shanks, Generalized Euler and class numbers, Math. Comp. 21 (1967), 689-694; 22 (1968), 699. [Annotated scanned copy] MATHEMATICA amax = 30; km0 = 10; Clear[cc]; L[a_, s_, km_] := Sum[JacobiSymbol[-a, 2 k+1]/(2k+1)^s, {k, 0, km}]; c[1, n_, km_] := 2(2n)! L[1, 2n+1, km] (2 / Pi)^(2n+1) // Round; c[a_ /; a>1, n_, km_] := (2n)! L[a, 2n+1, km] (2a / Pi)^(2n+1)/Sqrt[a] // Round; cc[km_] := cc[km] = Table[c[a, n, km], {a, 1, amax}, {n, 0, nmax}]; cc[km0]; cc[km = 2km0]; While[cc[km] != cc[km/2, km = 2km]]; A000362[a_] := cc[km][[a, 3]]; Table[A000362[a], {a, 1, amax} ] (* Jean-François Alcover, Feb 08 2016 *) CROSSREFS Cf. A000233, A000508. Sequence in context: A196340 A196319 A197304 * A196971 A197558 A218658 Adjacent sequences: A000359 A000360 A000361 * A000363 A000364 A000365 KEYWORD nonn,easy AUTHOR N. J. A. Sloane EXTENSIONS More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 02 2000 STATUS approved

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Last modified June 14 08:50 EDT 2024. Contains 373393 sequences. (Running on oeis4.)