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A186335
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A transform of the central binomial coefficients.
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2
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1, 1, 4, 7, 21, 46, 127, 309, 832, 2131, 5709, 15010, 40281, 107423, 289314, 778087, 2103361, 5687938, 15427099, 41880357, 113912236, 310148223, 845598389, 2307657222, 6304306171, 17237338021, 47170965082, 129181447969, 354027263457, 970851960736, 2664008539017
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OFFSET
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0,3
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COMMENTS
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Hankel transform is (-1)^n*A128056(n).
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LINKS
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FORMULA
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a(n)=sum{k=0..n, sum{j=0..n, binomial(k-j,n-k-j)*binomial(k,j)*A000984(n-k-j)}}.
Conjecture: n*a(n) +(-2*n+1)*a(n-1) +5*(-n+1)*a(n-2) +3*(2*n-3)*a(n-3) +5*(n-2)*a(n-4)=0. - R. J. Mathar, Feb 13 2015
a(n) ~ ((1+sqrt(21))/2)^(n + 3/2) / (2 * 21^(1/4) * sqrt(Pi*n)) . - Vaclav Kotesovec, Oct 30 2017
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MAPLE
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add(add(binomial(k-j, n-k-j)*binomial(k, j)*A000984(n-k-j), j=0..n), k=0..n) ;
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MATHEMATICA
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Table[Sum[Sum[Binomial[k-j, n-k-j]*Binomial[k, j]*Binomial[2*(n-k-j), n-k-j], {j, 0, n}], {k, 0, n}], {n, 0, 40}] (* Vaclav Kotesovec, Oct 30 2017 *)
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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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