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A053132
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One half of binomial coefficients C(2*n-4,5).
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6
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3, 28, 126, 396, 1001, 2184, 4284, 7752, 13167, 21252, 32890, 49140, 71253, 100688, 139128, 188496, 250971, 329004, 425334, 543004, 685377, 856152, 1059380, 1299480, 1581255, 1909908, 2291058, 2730756, 3235501, 3812256, 4468464
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OFFSET
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5,1
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LINKS
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FORMULA
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a(n) = binomial(2*n-4, 5)/2 if n >= 5 else 0.
G.f.: (x^5)*(3+10*x+3*x^2)/(1-x)^6.
Sum_{n>=5} 1/a(n) = 335/6 - 80*log(2).
Sum_{n>=5} (-1)^(n+1)/a(n) = 85/6 - 20*log(2). (End)
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MATHEMATICA
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Binomial[2*Range[5, 40]-4, 5]/2 (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {3, 28, 126, 396, 1001, 2184}, 40] (* Harvey P. Dale, Oct 25 2015 *)
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PROG
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(Haskell)
a053132 n = a053132_list !! (n-5)
a053132_list = f [1] $ drop 2 a000217_list where
f xs ts'@(t:ts) = (sum $ zipWith (*) xs ts') : f (t:xs) ts
(PARI) for(n=5, 50, print1(binomial(2*n-4, 5)/2, ", ")) \\ G. C. Greubel, Aug 26 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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