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%I #4 Jul 29 2014 20:41:49
%S 1,1,2,14,194,4114,118042,4274612,186932958,9577713250,562450162646,
%T 37232881004442,2742420824107648,222414345991567630,
%U 19691735781407563460,1889658596054736522248,195353325211864635176182,21643625444562045727620930
%N Column 0 of triangle A132610.
%C Triangle T=A132610 is generated by even matrix powers of itself such that row n+1 of T = row n of T^(2n) with appended '1' for n>=0 with T(0,0)=1.
%o (PARI) {a(n)=local(k=0,A=vector(n+1), p); A[1]=1; for(j=1, n-k-1, p=(n-1)^2-(n-j-1)^2; A=Vec((Polrev(A)+x*O(x^p))/(1-x))); A=Vec((Polrev(A)+x*O(x^p))/(1-x)); A[p+1]}
%o for(n=0,25,print1(a(n),", "))
%o (PARI) {a(n)=local(A=[1]);for(i=1,n,A=Vec(Ser(A)/(1-x)^(2*(#A)-3));A=concat(A,A[#A]));A[#A]}
%o for(n=0,25,print1(a(n),", "))
%Y Cf. A132610 (triangle); other columns: A132612, A132613; A132614.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 23 2007
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