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A053128
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Binomial coefficients C(2*n-5,6).
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7
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7, 84, 462, 1716, 5005, 12376, 27132, 54264, 100947, 177100, 296010, 475020, 736281, 1107568, 1623160, 2324784, 3262623, 4496388, 6096454, 8145060, 10737573, 13983816, 18009460, 22957480, 28989675, 36288252, 45057474, 55525372, 67945521, 82598880, 99795696
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OFFSET
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6,1
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COMMENTS
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a(n) = A053123(n,6), n >= 6; a(n) = 0, n=0..5, (seventh column of shifted Chebyshev's S-triangle, decreasing order).
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings).
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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FORMULA
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a(n) = binomial(2*n-5, 6) if n >= 6 else 0.
G.f.: (7+35*x+21*x^2+x^3)/(1-x)^7.
E.g.f.: (18900 - 16380*x + 6975*x^2 - 1935*x^3 + 390*x^4 - 60*x^5 + 8*x^6)*exp(x)/90. - G. C. Greubel, Aug 26 2018
a(n) = (n-5)*(n-4)*(n-3)*(2*n-9)*(2*n-7)*(2*n-5)/90. - Wesley Ivan Hurt, Mar 25 2020
Sum_{n>=6} 1/a(n) = 667/10 - 96*log(2).
Sum_{n>=6} (-1)^n/a(n) = 273/10 - 6*Pi - 12*log(2). (End)
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MATHEMATICA
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Table[Binomial[2*n-5, 6], {n, 6, 50}] (* G. C. Greubel, Aug 26 2018 *)
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PROG
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(PARI) for(n=6, 50, print1(binomial(2*n-5, 6), ", ")) \\ G. C. Greubel, Aug 26 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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