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%I #11 Oct 30 2017 05:52:06
%S 1,1,4,7,21,46,127,309,832,2131,5709,15010,40281,107423,289314,778087,
%T 2103361,5687938,15427099,41880357,113912236,310148223,845598389,
%U 2307657222,6304306171,17237338021,47170965082,129181447969,354027263457,970851960736,2664008539017
%N A transform of the central binomial coefficients.
%C Hankel transform is (-1)^n*A128056(n).
%F a(n)=sum{k=0..n, sum{j=0..n, binomial(k-j,n-k-j)*binomial(k,j)*A000984(n-k-j)}}.
%F 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
%F a(n) ~ ((1+sqrt(21))/2)^(n + 3/2) / (2 * 21^(1/4) * sqrt(Pi*n)) . - _Vaclav Kotesovec_, Oct 30 2017
%p A186335 := proc(n)
%p add(add(binomial(k-j,n-k-j)*binomial(k,j)*A000984(n-k-j),j=0..n),k=0..n) ;
%p end proc: # _R. J. Mathar_, Feb 13 2015
%t 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 *)
%K nonn,easy
%O 0,3
%A _Paul Barry_, Feb 18 2011
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