A046982 - OEIS

%I #15 May 21 2023 19:18:09

%S 1,2,2,8,10,64,244,2176,554,31744,202084,2830336,2162212,178946048,

%T 1594887848,30460116992,7756604858,839461371904,9619518701764,

%U 232711080902656,59259390118004,39611984424992768,554790995145103208,955693069653508096

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

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

%H T. D. Noe, <a href="/A046982/b046982.txt">Table of n, a(n) for n=0..100</a>

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

%t 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 *)

%t CoefficientList[Series[Tan[x+Pi/4],{x,0,30}],x]//Numerator (* _Harvey P. Dale_, May 21 2023 *)

%Y Cf. A046983.

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

%K nonn,frac,easy,nice

%O 0,2

%A _N. J. A. Sloane_