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 A046990 Numerators of Taylor series for log(1/cos(x)). Also from log(cos(x)). 10
 0, 1, 1, 1, 17, 31, 691, 10922, 929569, 3202291, 221930581, 9444233042, 56963745931, 29435334228302, 2093660879252671, 344502690252804724, 129848163681107301953, 868320396104950823611, 209390615747646519456961, 28259319101491102261334882 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 REFERENCES CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 42. L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 88. LINKS T. D. Noe, Table of n, a(n) for n = 0..100 FORMULA Let q(n) = Sum_{k=0..n-1} (-1)^k*A201637(n-1,k) then a(n) = numerator((-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: A046990:= n -> numer((-1)^(n-1)*q(2*n)/(2*n)!): seq(A046990(n), n=0..19);  # Peter Luschny, Nov 16 2012 MATHEMATICA Join[{0}, Numerator[Select[CoefficientList[Series[Log[1/Cos[x]], {x, 0, 40}], x], #!=0&]]] (* Harvey P. Dale, Jul 27 2011 *) a[n_] := Numerator[((-4)^n-(-16)^n)*BernoulliB[2*n]/2/n/(2*n)!]; a[0] = 0; Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Feb 11 2014, after Charles R Greathouse IV *) PROG (Sage) def A046990(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)).numer() [A046990(n) for n in (0..19)]  # Peter Luschny, Nov 16 2012 (PARI) a(n)=numerator(((-4)^n-(-16)^n)*bernfrac(2*n)/2/n/(2*n)!) \\ Charles R Greathouse IV, Nov 06 2013 CROSSREFS Cf. A046991, A002430, A050970. Sequence in context: A276592 A002425 A275994 * A059212 A058899 A038354 Adjacent sequences:  A046987 A046988 A046989 * A046991 A046992 A046993 KEYWORD nonn,easy,frac,nice AUTHOR STATUS approved

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Last modified October 21 04:44 EDT 2018. Contains 316404 sequences. (Running on oeis4.)