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A078818
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a(n) = 30*binomial(2n,n)/(n+3).
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4
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10, 15, 36, 100, 300, 945, 3080, 10296, 35100, 121550, 426360, 1511640, 5408312, 19501125, 70794000, 258529200, 949074300, 3500409330, 12964479000, 48198087000, 179799820200, 672822343050, 2524918756464, 9500112378000, 35830670759000, 135439935469020
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OFFSET
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0,1
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LINKS
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FORMULA
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D-finite with recurrence a(n) = a(n-1)*(4n^2+6n-4)/(n^2+3n) = A078817(n, 2) = 5*A007946(n)/(2n+1) = 30*A000984(n)/(n+3).
Sum_{n>=0} 1/a(n) = 4*Pi/(135*sqrt(3)) + 7/45.
Sum_{n>=0} (-1)^n/a(n) = 9/125 - 32*log(phi)/(375*sqrt(5)), where phi is the golden ratio (A001622). (End)
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EXAMPLE
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a(5) = 30*binomial(10,5)/8 = 945.
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MATHEMATICA
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Table[(30 Binomial[2 n, n] / (n + 3)), {n, 0, 30}] (* Vincenzo Librandi, Aug 11 2018 *)
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PROG
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(GAP) List([0..30], n->30*Binomial(2*n, n)/(n+3)); # Muniru A Asiru, Aug 09 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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