%I A160568
%S A160568 1,0,1,3,1,9,19,18,91,165,271,990,1765,3843,11467,21630,53299,140724,
%T A160568 287119,736101,1818235,3982044,10225117,24521409,56584243,143641017,
%U A160568 341948179,816095982,2045559205,4888806237,11897144767,29540684052
%N A160568 Diagonal sums of number triangle [k<=n]*C(n,2n-2k)3^(n-k)A000108(n-k).
%C A160568 Hankel transform is A160569(n+1).
%F A160568 G.f.: (1-x^2-sqrt(1-2x^2-12x^3+x^4))/(6*x^3);
%F A160568 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 A160568 a(n)=sum{k=0..floor(n/2), C(n-k,2n-4k)*3^(n-2k)*A000108(n-2k)};
%F A160568 a(n)=sum{k=0..n, C(n-k/2,2(n-k))*3^(n-k)*A000108(n-k)*(1+(-1)^k)/2};
%F A160568 a(n)=sum{k=0..n, C((n+k)/2,2k)*3^k*A000108(k)(1+(-1)^(n-k))/2}.
%Y A160568 Cf.: A025250, A160565.
%Y A160568 Sequence in context: A111568 A121489 A118793 this_sequence A157403 A105951 
               A038202
%Y A160568 Adjacent sequences: A160565 A160566 A160567 this_sequence A160569 A160570 
               A160571
%K A160568 easy,nonn
%O A160568 0,4
%A A160568 Paul Barry (pbarry(AT)wit.ie), May 19 2009