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A008294 Triangle of coefficients in expansion of D^n (sec x) / sec x in powers of tan x. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 19 05:01 EDT 2018. Contains 316336 sequences. (Running on oeis4.)