A064073 Generalized tangent number d(8,n).

8, 1408, 739328, 806453248, 1506300919808, 4297849713983488, 17390688314209599488, 94727563504456856240128, 668321603392783694711226368, 5928595592752632717848942215168, 64586438563324327821773422563688448, 847680268223550650928681687352090820608

Offset: 1

Author

Eric W. Weisstein, Aug 31 2001

Keywords

• nonn
• easy

Links

• Lars Blomberg, Table of n, a(n) for n = 1..177
• 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
• Eric Weisstein's World of Mathematics, Tangent Number.

Crossrefs

Cf. A000464, A064073, A064069, A349267, A349264.

Programs

Maple

egf := sec(8*x)*2*sin(4*x): ser := series(egf, x, 24):
seq((2*n-1)!*coeff(ser, x, 2*n-1), n = 1..10); # Peter Luschny, Nov 21 2021

Formula

E.g.f.: Sum_{k>0} a(k)x^(2k-1)/(2k-1)! = 2*sin(4x)/cos(8x).

a(n) = 2^(4n-1) * A000464(n-1).

a(n) = (2*n-1)!*[x^(2*n-1)](sec(8*x)*2*sin(4*x)). - Peter Luschny, Nov 21 2021