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 A000318 Generalized tangent numbers d(4,n). (Formerly M3713 N1517) 4

%I M3713 N1517

%S 4,128,16384,4456448,2080374784,1483911200768,1501108249821184,

%T 2044143848640217088,3605459138582973251584,7995891855149741436305408,

%U 21776918737280678860353961984,71454103701490016776039304265728

%N Generalized tangent numbers d(4,n).

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A000318/b000318.txt">Table of n, a(n) for n = 1..100</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 D. Shanks, <a href="/A000003/a000003.pdf">Generalized Euler and class numbers</a>, Math. Comp. 21 (1967), 689-694; 22 (1968), 699. [Annotated scanned copy]

%F a(n) = 2^(4n-2) * A000182(n).

%F The g.f. has the following continued fraction expansion: g.f. = [4, b(0), c(0), b(1), c(1), b(2), c(2), ...] where b(n) = (Sum_{k=0..n} 1/(2*k+1))^2 / (128*(n+1)*x), c(n) = -4/((2*n+3)*(Sum_{k=0..n} 1/(2*k+1))*(Sum_{k=0..n+1} 1/(2*k+1))) and each convergent of this continued fraction is a Padé approximant of the McLaurin series Sum_{k>=1} a(n)*x^(n-1). - _Thomas Baruchel_, Oct 19 2005

%t nn = 30; t = Rest@Union[Range[0, nn - 1]! CoefficientList[Series[Tan[x], {x, 0, nn}], x]]; t2 = t*2^Range[2, 2*nn, 4] (* _T. D. Noe_, Jun 19 2012 *)

%Y Cf. A000182, A000191.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_

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

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Last modified April 23 13:56 EDT 2021. Contains 343204 sequences. (Running on oeis4.)