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A104474
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a(n) = binomial(n+3,3)*binomial(n+7,3).
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1
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35, 224, 840, 2400, 5775, 12320, 24024, 43680, 75075, 123200, 194480, 297024, 440895, 638400, 904400, 1256640, 1716099, 2307360, 3059000, 4004000, 5180175, 6630624, 8404200, 10556000, 13147875, 16248960, 19936224, 24295040, 29419775
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) = (1/36)*(n+1)*(n+2)*(n+3)*(n+5)*(n+6)*(n+7).
G.f.: ( -35+21*x-7*x^2+x^3 ) / (x-1)^7 . - R. J. Mathar, Nov 30 2015
Sum_{n>=0} 1/a(n) = 7/200.
Sum_{n>=0} (-1)^n/a(n) = 1/40. (End)
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EXAMPLE
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a(0): C(0+3,3)*C(0+7,3) = C(3,3)*C(7,3) = 1*35 = 35.
a(7): C(7+3,3)*C(7+7,3) = C(10,3)*(14,3) = 120*364 = 43680.
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MATHEMATICA
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f[n_] := Binomial[n + 3, 3]Binomial[n + 7, 3]; Table[ f[n], {n, 0, 28}] (* Robert G. Wilson v, Apr 20 2005 *)
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PROG
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(PARI) vector(30, n, n--; binomial(n+3, 3)*binomial(n+7, 3)) \\ Michel Marcus, Jul 31 2015
(Magma) [Binomial(n+3, 3)*Binomial(n+7, 3): n in [0..30]]; // Vincenzo Librandi, Jul 31 2015
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CROSSREFS
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KEYWORD
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easy,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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