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 A000192 Generalized Euler numbers c(6,n). (Formerly M2167 N0865) 9
 2, 46, 7970, 3487246, 2849229890, 3741386059246, 7205584123783010, 19133892392367261646, 67000387673723462963330, 299131045427247559446422446, 1658470810032820740402966226850, 11179247066648898992009055586869646, 90035623994788132387893239340761189570 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 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 Sean A. Irvine, Table of n, a(n) for n = 0..250 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, Euler Number. FORMULA E.g.f.: 2*cos(3*x) / (2*cos(4*x) - 1). - F. Chapoton, Oct 06 2020 a(n) = (2*n)!*[x^(2*n)](sec(6*x)*(cos(x) + cos(5*x))). - Peter Luschny, Nov 21 2021 a(n) ~ 2^(6*n + 5/2) * 3^(2*n + 1/2) * n^(2*n + 1/2) / (Pi^(2*n + 1/2) * exp(2*n)). - Vaclav Kotesovec, Apr 15 2022 MAPLE egf := sec(6*x)*(cos(x) + cos(5*x)): ser := series(egf, x, 24): seq((2*n)!*coeff(ser, x, 2*n), n = 0..10); # Peter Luschny, Nov 21 2021 MATHEMATICA L[ a_, s_, t_:10000 ] := Plus@@Table[ N[ JacobiSymbol[ -a, 2k+1 ](2k+1)^(-s), 30 ], {k, 0, t} ]; c[ a_, n_, t_:10000 ] := (2n)!/Sqrt[ a ](2a/Pi)^(2n+1)L[ a, 2n+1, t ] (* Eric W. Weisstein, Aug 30 2001 *) PROG (Sage) t = PowerSeriesRing(QQ, 't', default_prec=24).gen() f = 2 * cos(3 * t) / (2 * cos(4 * t) - 1) f.egf_to_ogf().list()[::2] # F. Chapoton, Oct 06 2020 CROSSREFS Cf. A000187, A000191, A000411, A001587, A349264. Sequence in context: A074041 A277554 A000191 * A196197 A273380 A124690 Adjacent sequences: A000189 A000190 A000191 * A000193 A000194 A000195 KEYWORD nonn,easy AUTHOR N. J. A. Sloane EXTENSIONS More terms from Eric W. Weisstein, Aug 30 2001 STATUS approved

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Last modified October 4 09:13 EDT 2023. Contains 365873 sequences. (Running on oeis4.)