This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A046991 #31 Jan 02 2025 12:46:54
%S A046991 1,2,12,45,2520,14175,935550,42567525,10216206000,97692469875,
%T A046991 18561569276250,2143861251406875,34806217964017500,
%U A046991 48076088562799171875,9086380738369043484375,3952575621190533915703125,3920955016221009644377500000,68739242628124575327993046875
%N A046991 Denominators of Taylor series for log(1/cos(x)). Also from log(cos(x)).
%D A046991 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 88.
%D A046991 CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 42.
%D A046991 Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 32, equation 32:6:3 at page 301.
%H A046991 T. D. Noe, <a href="/A046991/b046991.txt">Table of n, a(n) for n = 0..100</a>
%H A046991 Index entries for <a href="/index/Be#Bernoulli">Bernoulli numbers</a> B(2n)
%F A046991 A046990(n)/a(n) = 2^(2n-1) *(2^(2n) -1) *abs(B(2n)) / ((2n)! *n).
%F A046991 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
%e A046991 log(1/cos(x)) = 1/2*x^2+1/12*x^4+1/45*x^6+17/2520*x^8+31/14175*x^10+...
%e A046991 log(cos(x)) = -(1/2*x^2+1/12*x^4+1/45*x^6+17/2520*x^8+31/14175*x^10+...).
%p A046991 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)!):
%p A046991 seq(A046991(n),n=0..17); # _Peter Luschny_, Nov 16 2012
%t A046991 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_ *)
%t A046991 Take[Denominator[CoefficientList[Series[Log[1/Cos[x]],{x,0,40}],x]],{1,-1,2}] (* _Harvey P. Dale_, Jan 18 2020 *)
%o A046991 (Sage)
%o A046991 def A046991(n):
%o A046991 def q(n):
%o A046991 return add((-1)^k*A173018(n-1, k) for k in (0..n-1))
%o A046991 return ((-1)^(n-1)*q(2*n)/factorial(2*n)).denom()
%o A046991 [A046991(n) for n in (0..17)] # _Peter Luschny_, Nov 16 2012
%o A046991 (PARI) a(n)=denominator(((-4)^n-(-16)^n)*bernfrac(2*n)/2/n/(2*n)!) \\ _Charles R Greathouse IV_, Nov 06 2013
%Y A046991 Cf. A046990, B(2n) = A027641(2n) / A027642(2n).
%K A046991 nonn,easy,frac,nice
%O A046991 0,2
%A A046991 _N. J. A. Sloane_