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Generalized tangent number d(8,n).
5

%I #24 Nov 22 2021 02:36:02

%S 8,1408,739328,806453248,1506300919808,4297849713983488,

%T 17390688314209599488,94727563504456856240128,

%U 668321603392783694711226368,5928595592752632717848942215168,64586438563324327821773422563688448,847680268223550650928681687352090820608

%N Generalized tangent number d(8,n).

%H Lars Blomberg, <a href="/A064073/b064073.txt">Table of n, a(n) for n = 1..177</a>

%H D. Shanks, <a href="http://dx.doi.org/10.1090/S0025-5718-1967-0223295-5">Generalized Euler and class numbers</a>. Math. Comp. 21 (1967) 689-694.

%H D. Shanks, <a href="http://dx.doi.org/10.1090/S0025-5718-1968-0227093-9">Corrigenda to: "Generalized Euler and class numbers"</a>, Math. Comp. 22 (1968), 699

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TangentNumber.html">Tangent Number</a>.

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

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

%F a(n) = (2*n-1)!*[x^(2*n-1)](sec(8*x)*2*sin(4*x)). - _Peter Luschny_, Nov 21 2021

%p egf := sec(8*x)*2*sin(4*x): ser := series(egf, x, 24):

%p seq((2*n-1)!*coeff(ser, x, 2*n-1), n = 1..10); # _Peter Luschny_, Nov 21 2021

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

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Aug 31 2001