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A211867
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a(n) = A097609(2*n-1,n), n>0; a(0)=1.
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1
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1, 0, 2, 3, 18, 50, 215, 735, 2898, 10668, 41202, 156090, 601623, 2308878, 8923343, 34487453, 133749330, 519277512, 2020262660, 7869597840, 30699524018, 119894389380, 468768069882, 1834589752182, 7186572436887, 28175111736300, 110547143014050, 434049816801900
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: x*G'(x)/G(x), where G(x) is the g.f. of A055113.
G.f.: x * d/dx (log(sqrt(12*x+2*sqrt(1-4*x)+2)/4-sqrt(1-4*x)/4-1/4)).
a(n) = sum(j=0..n, C(2*j+n-1,j)*(-1)^(n+j)*C(2*n,n-j))/2, n>0; a(0)=1.
a(n) = Sum_{j=0..n/2} (binomial(2*n,j)*binomial(n-j-1,n-2*j))/2. - Vladimir Kruchinin, Oct 05 2015
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MAPLE
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a := n -> (-1)^n*binomial(2*n-1, n-1)*hypergeom([-n, n/2, (n+1)/2], [n, n+1], 4):
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MATHEMATICA
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a[n_] := ((-1)^(3*n)*(2*n)!*HypergeometricPFQ[{(n+1)/2, -n, n/2}, {n, n+1}, 4])/(2*n!^2); a[0]=1; Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Feb 13 2013, from A097609 *)
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PROG
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(PARI) a(n) = if(n==0, 1, sum(k=0, n/2, (binomial(2*n, k)*binomial(n-k-1, n-2*k))/2)); \\ Altug Alkan, Oct 05 2015
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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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