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%I #6 Sep 19 2018 06:14:48
%S 1,0,-1,-1,-2,-6,-14,-27,-39,-4,269,1415,5258,16321,43705,98459,
%T 163216,49326,-1120684,-6502098,-25711856,-83830889,-233926105,
%U -545916369,-932372648,-280663557,6802456973,40262637059,162298734532,538385811978
%N Sequence with a (1,-1) Somos-4 Hankel transform.
%C Hankel transform is A178081.
%H G. C. Greubel, <a href="/A178080/b178080.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{k=0..floor(n/2)} ( (C(n-k,k)/(n-2*k+1))*Sum_{i=0..k} C(k,i)*C(n-k-i-1,n-2*k-i)*3^(n-2k-i)*2^i*(-1)^(k-i) ).
%t Table[If[n == 0, 1, Sum[(Binomial[n-k, k]/(n-2*k+1))*Sum[Binomial[k, j]* Binomial[n-k-j-1, n-2*k-j]*3^(n-2*k-j)*2^j*(-1)^(k-j), {j, 0, k}], {k, 0, Floor[n/2]}] + ((1 + (-1)^n)*(-2/3)^(n/2))/2], {n, 0, 50}] (* _G. C. Greubel_, Sep 18 2018 *)
%o (PARI) a(n) = sum(k=0,floor(n/2), sum(j=0,k, (binomial(n-k,k)/(n-2*k+1)) *binomial(k,j)*binomial(n-k-j-1,n-2*k-j)*3^(n-2*k-j)*2^j*(-1)^(k-j)));
%o for(n=0,30, print1(a(n), ", ")) \\ _G. C. Greubel_, Sep 18 2018
%K easy,sign
%O 0,5
%A _Paul Barry_, May 19 2010
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