A113996 Column 4 of triangle A113993, also equals column 0 of A113983^5.

1, 5, 25, 125, 665, 3825, 23977, 164105, 1225225, 9954981, 87750065, 836288501, 8587255313, 94679407585, 1117195703729, 14064269132049, 188338637653329, 2675444736963557, 40212844609440521, 637967091730240877

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Example

A113983^5, the matrix 5th power of triangle A113983, begins:
1;
5,1;
25,10,1;
125,75,15,1;
665,525,155,20,1;
3825,3705,1425,265,25,1;
23977,27275,12765,3035,405,30,1;
164105,212879,116175,33105,5565,575,35,1;
1225225,1774905,1097311,360055,71665,9225,775,40,1; ...

Prog

(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]

Crossrefs

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

Sequence in context: A373281 A111993 A341266 * A340538 A062875 A140288

Adjacent sequences: A113993 A113994 A113995 * A113997 A113998 A113999

Keyword

nonn

Author

Paul D. Hanna, Nov 12 2005

Status

approved