A000488 Generalized tangent numbers d_(n,3). (Formerly M5024 N2167)

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

1,1

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 = 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 *)

Crossrefs

Cf. A000061, A000176, A000518.

Sequence in context: A155122 A094101 A034673 * A025759 A276257 A276097

Adjacent sequences: A000485 A000486 A000487 * A000489 A000490 A000491

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