%I #2 Mar 30 2012 18:37:07

%S 1,6,42,351,3470,39968,528306,7906598,132426050,2457643895,

%T 50110693656,1114365815786,26856942480503,697612318151050,

%U 19435260247394150,578255661792065917,18303904706366202568,614296560055922433760

%N Column 2 of triangle Q = A135885; also equals column 0 of Q^3 = A135893.

%e Triangle Q = A135885 begins:

%e 1;

%e 2, 1;

%e 6, 4, 1;

%e 25, 20, 6, 1;

%e 138, 126, 42, 8, 1;

%e 970, 980, 351, 72, 10, 1;

%e 8390, 9186, 3470, 748, 110, 12, 1; ...

%e where column k of Q equals column 0 of Q^(k+1) such that

%e column 0 of Q equals column 0 of P=A135880 shift left and Q=P^2.

%o (PARI) {a(n)=local(P=Mat(1),R,PShR);if(n==0,1,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]))));R=P*PShR; R=matrix(#P+1, #P+1, r,c, if(r>=c, if(r<#P+1,R[r,c], if(c==1,(P^2)[ #P,1],(P^(2*c-1))[r-c+1,1])))); P=matrix(#R, #R, r,c, if(r>=c, if(r<#R,P[r,c], (R^c)[r-c+1,1]))));(P^2)[n+3,3])}

%Y Cf. A135885 (Q), A135893 (Q^3), A135880; other columns: A135881, A135886.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Dec 15 2007