A132471 Triangle, read by rows, where diagonal m of T equals diagonal m-1 of matrix power T^m for m>1: T(n,k) = [T^(n-k)](n-1,k) for n>=k>0, with T(n,n)=1 and T(n+1,n)=n+1 for n>=0.

1, 1, 1, 2, 2, 1, 12, 4, 3, 1, 132, 30, 6, 4, 1, 2200, 384, 54, 8, 5, 1, 50020, 7300, 780, 84, 10, 6, 1, 1458576, 186620, 16500, 1344, 120, 12, 7, 1, 52443832, 6046600, 465240, 31120, 2100, 162, 14, 8, 1, 2262992496, 239321824, 16486512, 955000, 52600, 3072

Offset

0,4

Links

Table of n, a(n) for n=0..50.

Example

Triangle begins:
1;
1, 1;
2, 2, 1;
12, 4, 3, 1;
132, 30, 6, 4, 1;
2200, 384, 54, 8, 5, 1;
50020, 7300, 780, 84, 10, 6, 1;
1458576, 186620, 16500, 1344, 120, 12, 7, 1;
52443832, 6046600, 465240, 31120, 2100, 162, 14, 8, 1;
2262992496, 239321824, 16486512, 955000, 52600, 3072, 210, 16, 9, 1; ...
Matrix square, T^2, begins:
1;
2, 1;
6, 4, 1;
34, 14, 6, 1;
354, 88, 24, 8, 1;
5648, 1058, 162, 36, 10, 1; ...
where diagonal 1 of T^2 = diagonal 2 of T: [2,4,6,8,10,...].
Matrix cube, T^3, begins:
1;
3, 1;
12, 6, 1;
72, 30, 9, 1;
718, 198, 54, 12, 1;
10982, 2210, 384, 84, 15, 1; ...
where diagonal 2 of T^3 = diagonal 3 of T: [12,30,54,84,...].
Matrix fourth power, T^4, begins:
1;
4, 1;
20, 8, 1;
132, 52, 12, 1;
1300, 384, 96, 16, 1;
19148, 4148, 780, 152, 20, 1;
394412, 67664, 9072, 1344, 220, 24, 1; ...
where diagonal 3 of T^4 = diagonal 4 of T: [132,384,780,1344,..].

Prog

(PARI) T(n, k)=local(M=matrix(n, n, r, c, if(r>=c, T(r-1, c-1)))); if(n<k || k<0, 0, if(n==k, 1, if(n==k+1, n, (M^(n-k))[n, k+1])))

Crossrefs

Cf. A132472 (column 0), A132473 (column 1).

Sequence in context: A346078 A014846 A100942 * A130528 A132986 A019112

Adjacent sequences: A132468 A132469 A132470 * A132472 A132473 A132474

Keyword

nonn,tabl

Author

Paul D. Hanna, Aug 22 2007

Status

approved