A008294 Triangle of coefficients in expansion of D^n (sec x) / sec x in powers of tan x.

1, 1, 1, 2, 5, 6, 5, 28, 24, 61, 180, 120, 61, 662, 1320, 720, 1385, 7266, 10920, 5040, 1385, 24568, 83664, 100800, 40320, 50521, 408360, 1023120, 1028160, 362880, 50521, 1326122, 6749040, 13335840, 11491200, 3628800, 2702765, 30974526, 113760240

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

J. F. Barbero G., J. Salas and E. J. S. Villaseñor, Bivariate Generating Functions for a Class of Linear Recurrences. II. Applications, arXiv preprint arXiv:1307.5624 [math.CO], 2013-2015.

Dominique Foata and Guo-Niu Han, Multivariable Tangent and Secant q-derivative Polynomials. - N. J. A. Sloane, Oct 05 2012

J. Francon, Histoires de fichiers, RAIRO Informatique Théorique et Applications, 12 (1978), 49-62.

J. Francon, Histoires de fichiers, RAIRO Informatique Théorique et Applications, 12 (1978), 49-62. (Annotated scanned copy)

Gordon Haigh, A "natural" approach to Pick's theorem, Math. Gaz. 64 (1980), no. 429, 173-180.

Donald E. Knuth and Thomas J. Buckholtz, Computation of tangent, Euler and Bernoulli numbers, Math. Comp. 21 1967 663-688.

Formula

a(0, k) = delta(0, k); a(n+1, k) = k*a(n, k-1) + (k+1)*a(n, k+1).

Mathematica

nmax = 11; t[0, 0] = 1; t[0, k_] = 0; t[n_, k_] := t[n, k] = k*t[n-1, k-1] + (k+1)*t[n-1, k+1]; Flatten[ Table[ t[n, k-1], {n, 0, nmax}, {k, Mod[n, 2]+1, n+1, 2}]] (* Jean-François Alcover, Nov 08 2011 *)

Crossrefs

Cf. A008293. See A104035 for another version.

Sequence in context: A198231 A272207 A155947 * A019694 A233588 A113975

Adjacent sequences: A008291 A008292 A008293 * A008295 A008296 A008297

Keyword

easy,nonn,tabf,nice

Author

N. J. A. Sloane

Status

approved