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A001756
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a(n) = A059366(n,n-3) = A059366(n,3) for n >= 3, where the triangle A059366 arises from the expansion of a trigonometric integral.
(Formerly M4967 N2131)
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2
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15, 60, 450, 4500, 55125, 793800, 13097700, 243243000, 5016886875, 113716102500, 2808787731750, 75071235739500, 2158298027510625, 66409170077250000, 2177272076104125000, 75769068248423550000, 2789248824895091934375, 108288483790044745687500
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OFFSET
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3,1
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COMMENTS
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Previous 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) = n! * Sum_{k=0..n-3} (-1)^k * 2^(2*k-n) * binomial(n-3, k) * binomial(2*n-2*k, n-3) * binomial(n-2*k+3, n-k) for n >= 3. [Special case of a formula by Comtet, but corrected]
a(n) = 20 * binomial(2*n-6, n-3) * n!/2^n for n >= 3. [Special case of a formula due to Reinhard Zumkeller]
a(n) = binomial(-1/2, 3) * binomial(-1/2, n-3) * (-1)^n * n! * 2^n for n >= 3. (End)
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MATHEMATICA
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RecurrenceTable[{a[3]==15, a[n]==a[n-1]n (2n-7)/(n-3)}, a, {n, 20}] (* Harvey P. Dale, Nov 08 2011 *)
Join[{c = 15}, Table[c = c*n*(2*n - 7)/(n - 3), {n, 4, 20}]] (* T. D. Noe, Aug 10 2012 *)
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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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