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A053135
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Binomial coefficients C(2*n+6,6).
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7
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1, 28, 210, 924, 3003, 8008, 18564, 38760, 74613, 134596, 230230, 376740, 593775, 906192, 1344904, 1947792, 2760681, 3838380, 5245786, 7059052, 9366819, 12271512, 15890700, 20358520, 25827165, 32468436, 40475358, 50063860, 61474519, 74974368, 90858768
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OFFSET
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0,2
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COMMENTS
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Even-indexed members of seventh column of Pascal's triangle A007318.
Number of standard tableaux of shape (2n+1,1^6). - Emeric Deutsch, May 30 2004
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LINKS
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FORMULA
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G.f.: (1 + 21*x + 35*x^2 + 7*x^3)/(1-x)^7.
a(n) = binomial(2*n+6, 6) = A000579(2*n+6).
E.g.f.: (90 + 2430*x + 6975*x^2 + 5655*x^3 + 1710*x^4 + 204*x^5 + 8*x^6)* exp(x)/90. - G. C. Greubel, Sep 03 2018
Sum_{n>=0} 1/a(n) = 96*log(2) - 131/2.
Sum_{n>=0} (-1)^n/a(n) = 23/2 - 6*Pi + 12*log(2). (End)
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MAPLE
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MATHEMATICA
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Table[Binomial[2*n+6, 6], {n, 0, 30}] (* G. C. Greubel, Sep 03 2018 *)
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PROG
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(PARI) vector(30, n, n--; binomial(2*n+6, 6)) \\ G. C. Greubel, Sep 03 2018
(Magma) [Binomial(2*n+6, 6): n in [0..30]]; // G. C. Greubel, Sep 03 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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