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A241023
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Central terms of the triangle in A102413.
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4
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1, 4, 16, 76, 384, 2004, 10672, 57628, 314368, 1728292, 9560016, 53144172, 296642688, 1661529588, 9333781872, 52566230076, 296697618432, 1677889961028, 9505151782288, 53928746972812, 306393243712384, 1742920028025364, 9925790375394096, 56584659163097436
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = 2*Hyper2F1([-n, n], [1], -1) for n>0. - Peter Luschny, Aug 02 2014
a(n) = Sum_{k = 0..n} (-1)^(n-k)*(2^k)*binomial(2*k, k)*binomial(n+k-1, n-k).
a(n) = (-1)^(n+1) * 4*n * hypergeom([n+1, -n+1], [2], 2).
n*(2*n - 3)*a(n) = 4*(3*n^2 - 6*n + 2)*a(n-1) - (2*n - 1)*(n - 2)*a(n-2) with a(0) = 1 and a(1) = 4.
O.g.f.: Sum_{n >= 0} (2^n)*binomial(2*n,n)*x^n/(1 + x)^(2*n) = 1 + 4*x + 16*x^2 + 76*x^3 + 384*x^4 + .... (End)
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MATHEMATICA
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a[0] = 1; a[n_] := 4 Hypergeometric2F1[1 - n, n + 1, 1, -1];
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PROG
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(Haskell)
a241023 n = a102413 (2 * n) n
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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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