A046983 Denominators of Taylor series for tan(x + Pi/4).

1, 1, 1, 3, 3, 15, 45, 315, 63, 2835, 14175, 155925, 93555, 6081075, 42567525, 638512875, 127702575, 10854718875, 97692469875, 1856156927625, 371231385525, 194896477400625, 2143861251406875, 2900518163668125, 2275791174570375

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy
• nice

Examples

			1 + 2*x + 2*x^2 + (8/3)*x^3 + (10/3)*x^4 + (64/15)*x^5 + (244/45)*x^6 + ...
		

References

• G. W. Caunt, Infinitesimal Calculus, Oxford Univ. Press, 1914, p. 477.

Links

• T. D. Noe, Table of n, a(n) for n=0..100

Crossrefs

Cf. A046982.

Programs

Maple

A046983 := proc(n)
    coeftayl(tan(x+Pi/4),x=0,n) ;
    denom(%) ;
end proc: # R. J. Mathar, Jan 22 2017

Mathematica

nmax = 24; t[0, 1] = 1; t[0, ] = 0; t[n, k_] := t[n, k] = (k-1)*t[n-1, k-1] + (k+1)*t[n-1, k+1]; Denominator[ Table[ Sum[ t[n, k]/n!, {k, 0, n+1}], {n, 0, nmax} ]] (* Jean-François Alcover, Nov 09 2011 *)
CoefficientList[Series[Tan[x+Pi/4],{x,0,30}],x]//Denominator (* Harvey P. Dale, Sep 05 2023 *)