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 A000411 Generalized tangent numbers d(6,n). (Formerly M4312 N1805) 6
 6, 522, 152166, 93241002, 97949265606, 157201459863882, 357802951084619046, 1096291279711115037162, 4350684698032741048452486, 21709332137467778453687752842, 133032729004732721625426681085926, 982136301747914281420205946546842922, 8597768767880274820173388403096814519366 (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 Lars Blomberg, Table of n, a(n) for n = 1..184 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] FORMULA a(n) = (2*n-1)! * [x^(2*n-1)] 2*sin(3*x) / (2*cos(4*x) - 1). - F. Chapoton, Oct 06 2020 a(n) = (2*n-1)!*[x^(2*n-1)](sec(6*x)*(sin(x) + sin(5*x))). - Peter Luschny, Nov 21 2021 MAPLE egf := sec(6*x)*(sin(x) + sin(5*x)): ser := series(egf, x, 24): seq((2*n-1)!*coeff(ser, x, 2*n-1), n = 1..12); # Peter Luschny, Nov 21 2021 MATHEMATICA nmax = 15; km0 = 10; Clear[dd]; L[a_, s_, km_] := Sum[JacobiSymbol[-a, 2 k + 1]/(2 k + 1)^s, {k, 0, km}]; d[a_ /; a > 1, n_, km_] := (2 n - 1)! L[-a, 2 n, km] (2 a/Pi)^(2 n)/Sqrt[a] // Round; dd[km_] := dd[km] = Table[d[6, n, km], {n, 1, nmax}]; dd[km0]; dd[km = 2 km0]; While[dd[km] != dd[km/2, km = 2 km]]; A000411 = dd[km] (* Jean-François Alcover, Feb 08 2016 *) PROG (Sage) t = PowerSeriesRing(QQ, 't', default_prec=24).gen() f = 2 * sin(3 * t) / (2 * cos(4 * t) - 1) f.egf_to_ogf().list()[1::2] # F. Chapoton, Oct 06 2020 CROSSREFS Cf. A000192, A000320, A001587, A349264. Sequence in context: A250391 A003395 A222607 * A180431 A202967 A230330 Adjacent sequences: A000408 A000409 A000410 * A000412 A000413 A000414 KEYWORD nonn AUTHOR EXTENSIONS a(10)-a(12) from Lars Blomberg, Sep 07 2015 STATUS approved

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Last modified March 31 15:18 EDT 2023. Contains 361668 sequences. (Running on oeis4.)