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A092956
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a(n) = (2*n+2)!/((n+2)*n!).
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8
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1, 8, 90, 1344, 25200, 570240, 15135120, 461260800, 15878903040, 609493248000, 25812039052800, 1195656969830400, 60138698780160000, 3264143527636992000, 190165504623494400000, 11836497605427855360000, 783921372659482337280000
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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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a(n) = Sum_{k=1..n+1} Gamma(n+1+k)/Gamma(k). - Bruno Berselli, Mar 06 2013
Let E(x) = Sum_{n>=0} a(n)*x^(2*n)/n!, then E(x) = 2- E(0,x), where E(k,x) = 1 - x^2*(k+1)/( x^2*(k+1) + (k + 1 -x^2)*(k + 2 -x^2)/E(k+1,x) ); (continued fraction). - Sergei N. Gladkovskii, Oct 21 2013
G.f.: Hypergeometric2F1([2,2,3/2], [3], 4*x).
E.g.f.: 4*x*Hypergeometric2F1([5/2,3], [4], 4*x) + Hypergeometric2F1([3/2,2], [3], 4*x). (End)
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MAPLE
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a:=n->sum(mul (j-k+n, j=1..n), k=1..n): seq(a(n), n=1..17); # Zerinvary Lajos, Jun 04 2007
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MATHEMATICA
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Table[(2n+2)!/((n+2) n!), {n, 0, 16}] (* Bruno Berselli, Mar 06 2013 *)
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PROG
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(Magma) [Factorial(n+1)*Binomial(2*n+2, n): n in [0..20]]; // G. C. Greubel, Aug 11 2022
(SageMath) [factorial(n+1)*binomial(2*n+2, n) for n in (0..20)] # G. C. Greubel, Aug 11 2022
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CROSSREFS
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KEYWORD
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easy,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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