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 A000320 Generalized tangent numbers d(5,n). (Formerly M3722 N1521) 7
 4, 272, 55744, 23750912, 17328937984, 19313964388352, 30527905292468224, 64955605537174126592, 179013508069217017790464, 620314831396713435870789632, 2639743384489464189324523208704, 13533573366345611477262311433961472, 82274260343572247169162187576069586944 (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..189 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)](sec(5*x)*(sin(x) + sin(3*x))). - Peter Luschny, Nov 21 2021 MAPLE egf := sec(5*x)*(sin(x) + sin(3*x)): ser := series(egf, x, 26): seq((2*n-1)!*coeff(ser, x, 2*n-1), n = 1..13); # Peter Luschny, Nov 21 2021 MATHEMATICA nmax = 15; km0 = 10; Clear[dd]; L[a_, s_, km_] := Sum[JacobiSymbol[-a, 2 k + 1]/(2k+1)^s, {k, 0, km}]; d[a_ /; a>1, n_, km_] := (2n-1)! L[-a, 2n, km] (2a/Pi)^(2n)/Sqrt[a] // Round; dd[km_] := dd[km] = Table[d[5, n, km], {n, 1, nmax}]; dd[km0]; dd[km = 2km0]; While[dd[km] != dd[km/2, km = 2 km]]; A000320 = dd[km] (* Jean-François Alcover, Feb 07 2016 *) CROSSREFS Cf. A000318, A000187, A349265, A349264. Sequence in context: A108134 A221081 A340916 * A101758 A134786 A290225 Adjacent sequences: A000317 A000318 A000319 * A000321 A000322 A000323 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS Formula producing A000326, rather than this sequence, deleted by Sean A. Irvine, Sep 09 2010 a(10)-a(13) from Lars Blomberg, Sep 07 2015 STATUS approved

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Last modified February 21 10:23 EST 2024. Contains 370228 sequences. (Running on oeis4.)