A000518 Generalized tangent numbers d_(n,4). (Formerly M5432 N2361)

272, 24611, 515086, 4456448, 23750912, 93241002, 296327464, 806453248, 1951153920, 4300685074, 8787223186, 16878338048, 30768878848, 53624926972, 89982082488, 146028888064, 230022888960, 353194774434, 529896144586

Offset

1,1

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

Lars Blomberg, Table of n, a(n) for n = 1..1000

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

Mathematica

amax = 20; km0 = 10; Clear[dd]; L[a_, s_, km_] := Sum[ JacobiSymbol[ -a, 2 k + 1]/(2 k + 1)^s, {k, 0, km}]; d[1, n_, km_] := 2 (2 n - 1)! L[-1, 2 n, km] (2/Pi)^(2 n) // Round; d[a_ /; a > 1, n_, km_] := (2 n - 1)! L[-a, 2 n, km] (2 a/Pi)^(2 n)/Sqrt[a] // Round; dd[km_] := dd[km] = Table[d[a, 4, km], {a, 1, amax}]; dd[km0]; dd[km = 2 km0]; While[dd[km] != dd[km/2, km = 2 km]]; A000518 = dd[km] (* Jean-François Alcover, Feb 09 2016 *)

Crossrefs

Cf. A000061 for d_(n,1), A000176 for d_(n,2), A000488 for d_(n,3).

Sequence in context: A023907 A281691 A035842 * A230531 A283230 A280044

Adjacent sequences: A000515 A000516 A000517 * A000519 A000520 A000521

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 03 2000

Status

approved