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A001194
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a(n) = A059366(n,n-2) = A059366(n,2) for n >= 2, where the triangle A059366 arises in the expansion of a trigonometric integral.
(Formerly M2826 N1139)
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1
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3, 9, 54, 450, 4725, 59535, 873180, 14594580, 273648375, 5685805125, 129636356850, 3217338674550, 86331921100425, 2490343877896875, 76844896803675000, 2525635608280785000, 88081541838792376875, 3248654513701342370625
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OFFSET
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2,1
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COMMENTS
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Old name was: Expansion of an integral.
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, pp. 166-167.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = (2*n - 1)*a(n-1) - 3*(n - 1)*(2*n - 7)!! for n > 3. - Sean A. Irvine, Mar 23 2012
a(n) = 3*n*(n-1)*(2*n-4)!/(2^(n-1)*(n-2)!) for n >= 2. - Vaclav Kotesovec, Jan 05 2014
a(n) = binomial(-1/2, 2) * binomial(-1/2, n-2) * (-1)^n * n! * 2^n for n >= 2. - Petros Hadjicostas, May 13 2020
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MATHEMATICA
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Table[3*n*(n-1)*(2*n-4)!/(2^(n-1)*(n-2)!), {n, 2, 20}] (* Vaclav Kotesovec, Jan 05 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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