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A108079
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a(n) = Sum_{i=0..n} C(2n+i,n+i).
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0
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1, 5, 31, 195, 1231, 7798, 49596, 316767, 2031535, 13079352, 84504355, 547707394, 3559971156, 23197272140, 151495214536, 991348425879, 6498704675439, 42669773400220, 280567674704625, 1847219933032320, 12176178948740895, 80346934651630500
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OFFSET
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0,2
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LINKS
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FORMULA
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MATHEMATICA
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Table[Binomial[3 n + 1, n + 1] - Binomial[2 n, n - 1], {n, 0, 40}] (* Vincenzo Librandi, Oct 02 2015 *)
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PROG
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(Maxima)
B(x):=(2/sqrt(3*x))*sin((1/3)*asin(sqrt(27*x/4)))-1;
C(x):=(1-sqrt(1-4*x))/(2*x);
taylor(x*diff(1/x-1/B(x), x)+x*diff(B(x), x)/B(x)-x*diff(C(x), x), x, 0, 10); /* Vladimir Kruchinin, Oct 01 2015 */
(Magma) [Binomial(3*n+1, n+1)-Binomial(2*n, n-1): n in [0..25]]; // Vincenzo Librandi, Oct 02 2015
(PARI) a(n) = binomial(3*n+1, n+1)-binomial(2*n, n-1);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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