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A002299
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Binomial coefficients C(2*n+5,5).
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8
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1, 21, 126, 462, 1287, 3003, 6188, 11628, 20349, 33649, 53130, 80730, 118755, 169911, 237336, 324632, 435897, 575757, 749398, 962598, 1221759, 1533939, 1906884, 2349060, 2869685, 3478761, 4187106, 5006386, 5949147, 7028847, 8259888, 9657648, 11238513
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OFFSET
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0,2
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COMMENTS
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Number of standard tableaux of shape (2n+1,1^5). - Emeric Deutsch, May 30 2004
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LINKS
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J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math., Vol. 201, No. 1 (2006), pp. 143-179. [Th. 7.2(i), case a=1]
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FORMULA
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G.f.: (1+15*x+15*x^2+x^3)/(1-x)^6 = (1+x)*(x^2+14*x+1)/(1-x)^6.
E.g.f.: (30 + 600*x + 1275*x^2 + 730*x^3 + 140*x^4 + 8*x^5)*exp(x)/30. - G. C. Greubel, Nov 23 2017
Sum_{n>=0} 1/a(n) = 40*log(2) - 80/3. - Amiram Eldar, Jan 03 2022
a(n) = Sum_{0 <= i <= j <= n} (j+1)*(2*i+1)^2.
a(n) = (n+2)*(2*n+5)/(n*(2*n-1))*a(n-1) with a(0) := 1. (End)
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MATHEMATICA
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Table[Binomial[2*n + 5, 5], {n, 0, 50}] (* G. C. Greubel, Nov 23 2017 *)
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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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