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Conjecture: 2*(n+3)*a(n) + 4*(-3*n-4)*a(n-1) + (17*n-9)*a(n-2) + 2*(-2*n+5)*a(n-3) = 0. - R. J. Mathar, Aug 25 2013
a(n) = (3*binomial(2*n+2, n) + 5*binomial(2*n, n+2))/(n + 3). - Tani Akinari, Dec 01 2024
a := n -> (17*n^2 + 13*n + 6)*binomial(2*n, n)/((n + 1)*(n + 2)*(n + 3)): seq(a(n), n = 0..24); # Peter Luschny, Dec 01 2024
Cf. A000108.
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a(n) = (3*binomial(2*n+2,n)+5*binomial(2*n,n+2))/(n+3). - Tani Akinari, Dec 01 2024
(Maxima) a(n):=(3*binomial(2*n+2, n)+5*binomial(2*n, n+2))/(n+3); makelist(a(n), n, 0, 50);
/* Tani Akinari, Dec 01 2024 */
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Conjecture: 2*(n+3)*a(n) +4*(-3*n-4)*a(n-1) +(17*n-9)*a(n-2) +2*(-2*n+5)*a(n-3)=0. - R. J. Mathar, Aug 25 2013
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_N. J. A. Sloane (njas(AT)research.att.com), _, Jun 06 2002