login
Column 0 of triangular matrix A102225, in which row k is formed from the first differences of row (k-1) of its matrix square (A102228).
4

%I #5 Mar 30 2012 18:36:44

%S 1,1,2,3,7,17,75,346,4874,49047,3009094,69540959,19266759978,

%T 1145861630146,1316021940482105,231957006949639674,

%U 1000756528918141445755,578298169571294295021140

%N Column 0 of triangular matrix A102225, in which row k is formed from the first differences of row (k-1) of its matrix square (A102228).

%C Also equals column 0 of A102228 shift one place right.

%F a(n) = A102229(n-1) - A102227(n) for n>=2, where A102227 equals column 1 of A102225 and A102229 equals column 1 of A102228.

%o (PARI) {a(n)=local(A=matrix(1,1),B);A[1,1]=1; for(m=2,n+1,B=matrix(m,m);for(i=1,m, for(j=1,i, if(j==i,B[i,j]=1,if(j==1,B[i,j]=(A^2)[i-1,1], B[i,j]=(A^2)[i-1,j]-(A^2)[i-1,j-1]));));A=B);return(A[n+1,1])}

%Y Cf. A102225, A102227, A102228, A102229.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jan 01 2005