%I #7 Jun 13 2017 23:38:43

%S 1,5,25,125,665,3825,23977,164105,1225225,9954981,87750065,836288501,

%T 8587255313,94679407585,1117195703729,14064269132049,188338637653329,

%U 2675444736963557,40212844609440521,637967091730240877

%N Column 4 of triangle A113993, also equals column 0 of A113983^5.

%e A113983^5, the matrix 5th power of triangle A113983, begins:

%e 1;

%e 5,1;

%e 25,10,1;

%e 125,75,15,1;

%e 665,525,155,20,1;

%e 3825,3705,1425,265,25,1;

%e 23977,27275,12765,3035,405,30,1;

%e 164105,212879,116175,33105,5565,575,35,1;

%e 1225225,1774905,1097311,360055,71665,9225,775,40,1; ...

%o (PARI) a(n)=local(A,B);A=Mat(1);for(m=2,n+2,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==1 || j==i,B[i,j]=1, B[i,j]=A[i-1,j-1]+(A^2)[i-2,j-1] );));A=B);(A^5)[n+1,1]

%Y Cf. A113993, A113989 (column 1), A113994 (column 2), A113995 (column 3), A113997 (row sums); A113983.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Nov 12 2005