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A112328
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a(n) = (n+1)*binomial(2n+2,n+1)-3*4^n+binomial(2n,n).
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2
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2, 18, 108, 562, 2724, 12660, 57240, 253842, 1109748, 4798780, 20572392, 87580308, 370706408, 1561573032, 6551178288, 27387484242, 114146434068, 474476717292, 1967642119368, 8142727008732, 33634295542968, 138696447565272
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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G.f.: 4z[2-sqrt(1-4z)]/[(1-4z)^(3/2)(1+sqrt(1-4z)]
32*(2*n^2 - 9*n + 10)*a(n - 3) - 8*(2*n^2 - 14*n + 15)*a(n - 2) - 2*(2*n^2 + 3*n - 5)*a(n - 1) + n*(n - 1)*a(n) = 0. - Robert Israel, Sep 19 2019
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MAPLE
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a:=n->(n+1)*binomial(2*n+2, n+1)-3*4^n+binomial(2*n, n): seq(a(n), n=1..25);
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MATHEMATICA
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a[n_]:=(n+1)*Binomial[2n+2, n+1]-3*4^n+Binomial[2n, n]; Array[a, 22] (* Stefano Spezia, Sep 20 2019 *)
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PROG
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(PARI) a(n) = (n+1)*binomial(2*n+2, n+1)-3*4^n+binomial(2*n, n); \\ Michel Marcus, Sep 20 2019
(Magma) [(n+1)*Binomial(2*n+2, n+1)-3*4^n+Binomial(2*n, n):n in [1..22]]; // Marius A. Burtea, Sep 20 2019
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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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