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 A046991 Denominators of Taylor series for log(1/cos(x)). Also from log(cos(x)). 3
 1, 2, 12, 45, 2520, 14175, 935550, 42567525, 10216206000, 97692469875, 18561569276250, 2143861251406875, 34806217964017500, 48076088562799171875, 9086380738369043484375, 3952575621190533915703125, 3920955016221009644377500000, 68739242628124575327993046875 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 88. CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 42. LINKS T. D. Noe, Table of n, a(n) for n = 0..100 Index entries for Bernoulli numbers B(2n) FORMULA A046990(n)/a(n) = 2^(2n-1) *(2^(2n) -1) *abs(B(2n)) / ((2n)! *n). Let q(n) = Sum_{k=0..n-1} (-1)^k*A201637(n-1,k) then a(n) = denominator((-1)^(n-1)*q(2*n)/(2*n)!). - Peter Luschny, Nov 16 2012 EXAMPLE log(1/cos(x)) = 1/2*x^2+1/12*x^4+1/45*x^6+17/2520*x^8+31/14175*x^10+... log(cos(x)) = -(1/2*x^2+1/12*x^4+1/45*x^6+17/2520*x^8+31/14175*x^10+...). MAPLE q:= proc(n) add((-1)^k*combinat[eulerian1](n-1, k), k=0..n-1) end: A046991:= n -> denom((-1)^(n-1)*q(2*n)/(2*n)!): seq(A046991(n), n=0..17); # Peter Luschny, Nov 16 2012 MATHEMATICA a[n_] := Denominator[((-4)^n-(-16)^n)*BernoulliB[2*n]/2/n/(2*n)!]; a[0] = 0; Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Feb 11 2014, after Charles R Greathouse IV *) Take[Denominator[CoefficientList[Series[Log[1/Cos[x]], {x, 0, 40}], x]], {1, -1, 2}] (* Harvey P. Dale, Jan 18 2020 *) PROG (Sage) def A046991(n): def q(n): return add((-1)^k*A173018(n-1, k) for k in (0..n-1)) return ((-1)^(n-1)*q(2*n)/factorial(2*n)).denom() [A046991(n) for n in (0..17)] # Peter Luschny, Nov 16 2012 (PARI) a(n)=denominator(((-4)^n-(-16)^n)*bernfrac(2*n)/2/n/(2*n)!) \\ Charles R Greathouse IV, Nov 06 2013 CROSSREFS Cf. A046990, B(2n) = A027641(2n) / A027642(2n). Sequence in context: A276294 A066258 A123771 * A188982 A061990 A006742 Adjacent sequences: A046988 A046989 A046990 * A046992 A046993 A046994 KEYWORD nonn,easy,frac,nice AUTHOR N. J. A. Sloane STATUS approved

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Last modified July 18 06:54 EDT 2024. Contains 374377 sequences. (Running on oeis4.)