%I #2 Mar 30 2012 18:37:08

%S 1,4,26,232,2657,37405,627435,12248365,273211787,6862775083,

%T 191840407156,5909873159107,199002812894375,7273866200397039,

%U 286882936292798852,12145886485652450131,549504341899436759416

%N Column 1 of triangle A136225; also equals column 0 of triangle A136230.

%C Equals column 1 of P^2 (A136225) and equals column 0 of V^2, where P = A136220 and V = A136230 are triangular matrices such that column k of V = column 0 of P^(3k+2) and column j of P^2 = column 0 of V^(j+1).

%o (PARI) /* Generate using matrix product recurrences of triangle P=A136220: */ {a(n)=local(P=Mat([1,0;1,1]),U,PShR);if(n>0,for(i=0,n+1, PShR=matrix(#P,#P, r,c, if(r>=c,if(r==c,1,if(c==1,0,P[r-1,c-1]))));U=P*PShR^2; U=matrix(#P+1, #P+1, r,c, if(r>=c, if(r<#P+1,U[r,c], if(c==1,(P^3)[ #P,1],(P^(3*c-1))[r-c+1,1])))); P=matrix(#U, #U, r,c, if(r>=c, if(r<#R,P[r,c], (U^c)[r-c+1,1])))));(P^2)[n+2,2]}

%Y Cf. A136226, A136225 (P^2), A136220 (P), A136230 (V); A136217.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 28 2008