A000362 Generalized class numbers c_(n,2). (Formerly M4016 N1664)

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

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