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A028340
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Coefficient of x^3 in expansion of (x+1)*(x+3)*...*(x+2*n-1).
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6
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1, 16, 230, 3480, 57379, 1038016, 20570444, 444647600, 10431670821, 264300628944, 7198061846898, 209814739262856, 6520139954328519, 215245451727154944, 7524314127912551832, 277705505168550027360, 10792700030471840300745, 440604294676004639627280
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OFFSET
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3,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{i=k+1..n} (-1)^(k+1-i)*2^(n-1)*binomial(i-1, k)*s1(n, i) with k = 3, where s1(n, i) are unsigned Stirling numbers of the first kind. - Victor Adamchik (adamchik(AT)ux10.sp.cs.cmu.edu), Jan 23 2001
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MATHEMATICA
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Table[Coefficient[Product[x + 2*k - 1, {k, 1, n}], x, 3], {n, 3, 50}] (* G. C. Greubel, Nov 24 2016 *)
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PROG
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(PARI) a(n) = polcoeff(prod(k=1, n, x+2*k-1), 3); \\ Michel Marcus, Nov 12 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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