A046982 Numerators of Taylor series for tan(x + Pi/4).

1, 2, 2, 8, 10, 64, 244, 2176, 554, 31744, 202084, 2830336, 2162212, 178946048, 1594887848, 30460116992, 7756604858, 839461371904, 9619518701764, 232711080902656, 59259390118004, 39611984424992768, 554790995145103208, 955693069653508096

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. A046983.

a(n) = 2^k * A050970(n), for some k>=0 (conjectured).

Programs

Mathematica

nmax = 23; 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]; Numerator[ 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]//Numerator (* Harvey P. Dale, May 21 2023 *)