A000518 Generalized tangent numbers d_(n,4).

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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

Crossrefs

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

Programs

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 *)

Extensions

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