A000488 Generalized tangent numbers d_(n,3).

16, 361, 3362, 16384, 55744, 152166, 355688, 739328, 1415232, 2529614, 4261454, 6885376, 10708160, 16054580, 23494584, 33554432, 46698624, 64037790, 86342918, 114163712, 149518720, 193356526, 246232840, 311635968, 390600000

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, A000176, A000518.

Programs

Mathematica

amax = 25; km0 = 10; 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, 3, km], {a, 1, amax}]; dd[km0]; dd[km = 2 km0]; While[dd[km] != dd[km/2, km = 2 km]]; A000488 = dd[km] (* Jean-François Alcover, Feb 08 2016 *)

Extensions

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