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A030056
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a(n) = binomial(2*n+1, n-6).
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4
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1, 15, 136, 969, 5985, 33649, 177100, 888030, 4292145, 20160075, 92561040, 417225900, 1852482996, 8122425444, 35240152720, 151532656696, 646626422970, 2741188875414, 11554258485616, 48459472266975
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internal format)
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OFFSET
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6,2
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LINKS
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FORMULA
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a(n+1) = a(n)*(2*n+2)*(2*n+3)/((n-5)*(n+8)). - Chai Wah Wu, Jan 26 2016
Sum_{n>=6} 1/a(n) = 40*Pi/(9*sqrt(3)) - 96827/13860.
Sum_{n>=6} (-1)^n/a(n) = 29248*log(phi)/(5*sqrt(5)) - 3486955/2772, where phi is the golden ratio (A001622). (End)
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MATHEMATICA
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Table[Binomial[2*n + 1, n - 6], {n, 6, 25}] (* Amiram Eldar, Jan 24 2022 *)
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PROG
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(Python)
from __future__ import division
for n in range(6, 501):
b = b*(2*n+2)*(2*n+3)//((n-5)*(n+8)) # Chai Wah Wu, Jan 26 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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