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FORMULA
| E.g.f.: exp(4*x)*(BesselI(0, 2*x)-BesselI(1, 2*x))^2. a(n) = Sum_{k=0..n} binomial(n, k)*binomial(2*k, k)/(k+1)*binomial(2*n-2*k, n-k)/(n-k+1) = 4^n*Sum_{k=0..n} (-4)^(-k)*binomial(n, k)*binomial(k, floor(k/2))*binomial(k+1, floor((k+1)/2)) = binomial(2*n, n)/(n+1)*hypergeom([ -n-1, -n, 1/2], [2, 1/2-n], -1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 01 2004
(n + 1)*(n + 2)*a(n) = 4*(3*n^2 + n - 1)*a(n - 1) - 32*(n - 1)^2*a(n - 2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 15 2004
a(n) = Sum_{k,0<=k<=n}binomial(n,k)*A000108(k)*A000108(n-k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 23 2006
A014330(n) = (4*A053175(n)-A053175(n+1)/4) / ((n+2)*2^n) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Jul 02 2010]
G.f.: (1-6*x)*hypergeom([1/2, 1/2],[2],16*x^2/(4*x-1)^2)/(2*x*(4*x-1)) - x*(8*x-1)*hypergeom([3/2, 3/2],[3],16*x^2/(4*x-1)^2)/(4*x-1)^3 + 1/(2*x) - Mark van Hoeij, Oct 25 2011.
E.g.f.: hypergeom([1/2],[2],4*x)^2, coinciding with the above given e.g.f. - Wolfdieter Lang, Jan 13 2012
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