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A104473
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a(n) = binomial(n+2,2)*binomial(n+6,2).
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1
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15, 63, 168, 360, 675, 1155, 1848, 2808, 4095, 5775, 7920, 10608, 13923, 17955, 22800, 28560, 35343, 43263, 52440, 63000, 75075, 88803, 104328, 121800, 141375, 163215, 187488, 214368, 244035, 276675, 312480, 351648, 394383, 440895, 491400, 546120, 605283, 669123
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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) = (1/4)*(n+1)*(n+2)*(n+5)*(n+6).
Sum_{n>=0} 1/a(n) = 43/450.
Sum_{n>=0} (-1)^n/a(n) = 16*log(2)/15 - 154/225. (End)
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EXAMPLE
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a(0) = C(0+2,2)*C(0+6,2) = C(2,2)*C(6,2) = 1*15 = 155.
a(10) = C(10+2,2)*C(10+6,2) = C(12,2)*(16,2) = 66*120 = 7920.
a(6) = 1*3*5 + 2*4*6 + 3*5*7 + 4*6*8 + 5*7*9 + 6*8*10 + 7*9*11 = 1848. - Bruno Berselli, Apr 28 2014
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MATHEMATICA
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f[n_] := Binomial[n + 2, 2] Binomial[n + 6, 2]; Table[f[n], {n, 0, 27}] (* Robert G. Wilson v, Apr 20 2005 *)
CoefficientList[Series[-3 (x^2 - 4 x + 5)/(x - 1)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 28 2014 *)
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PROG
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(Magma) [Binomial(n+2, 2)*Binomial(n+6, 2): n in [0..50]]; // Vincenzo Librandi, Apr 28 2014
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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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