A113114 Triangle T, read by rows, equal to the matrix 5th power of triangle A113106, which satisfies the recurrence: A113106(n,k) = [A113106^5](n-1,k-1) + [A113106^5](n-1,k).

1, 5, 1, 85, 30, 1, 4985, 2435, 155, 1, 1082905, 662060, 61310, 780, 1, 930005021, 671754405, 80861810, 1528810, 3905, 1, 3306859233805, 2718081933706, 399334065655, 9987138060, 38169435, 19530, 1, 50220281721033905

Offset: 0

Author

Paul D. Hanna, Oct 14 2005

Keywords

• nonn
• tabl

Comments

Column 0 equals A113107 shift one place left.

Examples

			Triangle begins:
1;
5,1;
85,30,1;
4985,2435,155,1;
1082905,662060,61310,780,1;
930005021,671754405,80861810,1528810,3905,1;
3306859233805,2718081933706,399334065655,9987138060,38169435,19530,1;
		

Crossrefs

Cf. A113106, A113108, A113110, A113112.

Programs

PARI

{T(n,k)=local(M=matrix(n+1,n+1));for(r=1,n+1, for(c=1,r, M[r,c]=if(r==c,1,if(c>1,(M^5)[r-1,c-1])+(M^5)[r-1,c]))); return((M^5)[n+1,k+1])}