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A189177
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Diagonal sums of the Riordan matrix (1+x/sqrt(1-4*x),(1-sqrt(1-4*x))/2) (A189175).
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2
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1, 1, 3, 8, 26, 88, 311, 1125, 4139, 15411, 57901, 219070, 833509, 3185834, 12223298, 47048989, 181596815, 702589992, 2723964698, 10580344863, 41163089721, 160380285133, 625698670720
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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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a(n) = sum(binomial(2*n-3*k,n-k)*(n^2-n*k-k^2-k)/((2*n-3*k)*(2*n-3*k-1)),k=0..floor(n/2))), for n>=3.
G.f.: (2-9*x+3*x^2+4*x^3+(x+3*x^2)*sqrt(1-4*x))/(2*(1-4*x)(1-x+x^3)).
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MATHEMATICA
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T[n_, k_]=If[n==k, 1, Binomial[2n-k, n-k](n^2+n k-k^2-k)/((2n-k)(2n-k-1))]
Table[Sum[T[n-k, k], {k, 0, Floor[n/2]}], {n, 0, 22}]
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PROG
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(Maxima) T(n, k):=if n=k then 1 else binomial(2*n-k, n-k)*(n^2+n*k-k^2-k)/((2*n-k)*(2*n-k-1));
makelist(sum(T(n-k, k), k, 0, floor(n/2)), n, 0, 22);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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