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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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5
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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
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internal format)
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OFFSET
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0,4
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LINKS
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J. Francon, Histoires de fichiers, RAIRO Informatique Théorique et Applications, 12 (1978), 49-62. (Annotated scanned copy)
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FORMULA
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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
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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 *)
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CROSSREFS
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KEYWORD
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easy,nonn,tabf,nice
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AUTHOR
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STATUS
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approved
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