A000176 Generalized tangent numbers d_(n,2).

2, 11, 46, 128, 272, 522, 904, 1408, 2160, 3154, 4306, 5888, 7888, 10012, 12888, 16384, 19680, 24354, 29866, 34816, 41888, 49778, 56744, 66816, 78000, 87358, 100602, 115712, 128112, 145804, 165712, 180224, 203040, 228964, 246932, 276480

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Consider the Dirichlet series L_a(s) = sum_{k>=0} (-a|2k+1) / (2k+1)^s, where (-a|2k+1) is the Jacobi symbol. Then the numbers d_(a,n) are defined by L_a(2n)= (Pi/(2a))^(2n)*sqrt(a)* d_(a,n)/ (2n-1)! for a>1 and n=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

• Sean A. Irvine, Table of n, a(n) for n = 1..10000
• D. Shanks, Generalized Euler and class numbers. Math. Comp. 21 (1967) 689-694.
• D. Shanks, Corrigenda to: "Generalized Euler and class numbers", Math. Comp. 21 (1967), 689-694; 22 (1968), 699.

Crossrefs

Cf. A000061 for d_(n,1), A000488 for d_(n,3), A000518 for d_(n,4).

Extensions

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