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A053137
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Binomial coefficients C(2*n+8,8).
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6
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1, 45, 495, 3003, 12870, 43758, 125970, 319770, 735471, 1562275, 3108105, 5852925, 10518300, 18156204, 30260340, 48903492, 76904685, 118030185, 177232627, 260932815, 377348994, 536878650, 752538150, 1040465790, 1420494075, 1916797311, 2558620845, 3381098545
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OFFSET
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0,2
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COMMENTS
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Even-indexed members of ninth column of Pascal's triangle A007318.
Number of standard tableaux of shape (2n+1,1^8). - Emeric Deutsch, May 30 2004
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LINKS
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FORMULA
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a(n) = binomial(2*n+8, 8) = A000581(2*n+8).
G.f.: (1+36*x+126*x^2+84*x^3+9*x^4) / (1-x)^9 = (1+3*x) * (3*x^3+27*x^2+33*x+1) / (1-x)^9.
Sum_{n>=0} 1/a(n) = 512*log(2) - 5308/15.
Sum_{n>=0} (-1)^n/a(n) = 16*Pi + 32*log(2) - 1072/15. (End)
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MATHEMATICA
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Table[Binomial[2*n+8, 8], {n, 0, 30}] (* G. C. Greubel, Sep 03 2018 *)
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 45, 495, 3003, 12870, 43758, 125970, 319770, 735471}, 30] (* Harvey P. Dale, Jul 02 2022 *)
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PROG
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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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