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%I #2 Mar 30 2012 18:59:25
%S 1,0,1,3,1,9,19,18,91,165,271,990,1765,3843,11467,21630,53299,140724,
%T 287119,736101,1818235,3982044,10225117,24521409,56584243,143641017,
%U 341948179,816095982,2045559205,4888806237,11897144767,29540684052
%N Diagonal sums of number triangle [k<=n]*C(n,2n-2k)3^(n-k)A000108(n-k).
%C Hankel transform is A160569(n+1).
%F G.f.: (1-x^2-sqrt(1-2x^2-12x^3+x^4))/(6*x^3);
%F G.f.: 1/(1-x^2-3*x^3/(1-x^2-3*x^3/(1-x^2-3*x^3/(1-x^2-3*x^3/(1-... (continued fraction).
%F a(n)=sum{k=0..floor(n/2), C(n-k,2n-4k)*3^(n-2k)*A000108(n-2k)};
%F a(n)=sum{k=0..n, C(n-k/2,2(n-k))*3^(n-k)*A000108(n-k)*(1+(-1)^k)/2};
%F a(n)=sum{k=0..n, C((n+k)/2,2k)*3^k*A000108(k)(1+(-1)^(n-k))/2}.
%Y Cf.: A025250, A160565.
%K easy,nonn
%O 0,4
%A _Paul Barry_, May 19 2009
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