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A008294
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Triangle of coefficients in expansion of D^n (sec x) / sec x in powers of tan x.
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4
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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; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| Haigh, Gordon; A "natural" approach to Pick's theorem. Math. Gaz. 64 (1980), no. 429, 173-180.
Knuth, D. E.; Buckholtz, Thomas J. Computation of tangent, Euler and Bernoulli numbers. Math. Comp. 21 1967 663-688.
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FORMULA
| a(0, k)=delta(0, k); a(n+1, k)=k*a(n, k-1)+(k+1)a(n, k+1).
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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}]] (* From Jean-François Alcover, Nov 08 2011 *)
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CROSSREFS
| Cf. A008293. See A104 035 for another version.
Sequence in context: A161017 A198231 A155947 * A019694 A113975 A035585
Adjacent sequences: A008291 A008292 A008293 * A008295 A008296 A008297
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KEYWORD
| easy,nonn,tabl,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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