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 A000318 Generalized tangent numbers d(4,n). (Formerly M3713 N1517) 6
 4, 128, 16384, 4456448, 2080374784, 1483911200768, 1501108249821184, 2044143848640217088, 3605459138582973251584, 7995891855149741436305408, 21776918737280678860353961984, 71454103701490016776039304265728, 278008871543597996197497752082448384 (list; graph; refs; listen; history; text; internal format)
 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 T. D. Noe, Table of n, a(n) for n = 1..100 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 D. Shanks, Generalized Euler and class numbers, Math. Comp. 21 (1967), 689-694; 22 (1968), 699. [Annotated scanned copy] Eric Weisstein's World of Mathematics, Padé approximants. FORMULA a(n) = 2^(4n-2) * A000182(n). 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 Maclaurin series Sum_{k>=1} a(n)*x^(n-1). - Thomas Baruchel, Oct 19 2005 a(n) = (2*n-1)!*[x^(2*n-1)](sec(4*x)*sin(4*x)). - Peter Luschny, Nov 21 2021 MAPLE egf := sec(4*x)*sin(4*x): ser := series(egf, x, 26): seq((2*n-1)!*coeff(ser, x, 2*n-1), n = 1..12); # Peter Luschny, Nov 21 2021 MATHEMATICA 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 *) CROSSREFS Cf. A000182, A000191, A000490, A349264. Sequence in context: A013823 A321233 A130318 * A229385 A141367 A141368 Adjacent sequences: A000315 A000316 A000317 * A000319 A000320 A000321 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 03 2000 STATUS approved

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Last modified December 6 10:23 EST 2022. Contains 358630 sequences. (Running on oeis4.)