A098446 Triangle, read by rows, such that T(n,k) equals the k-th term of the convolution of the (n-1)-th diagonal with the k-th row of this triangle.

1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 9, 9, 1, 1, 5, 16, 30, 24, 1, 1, 6, 25, 70, 115, 77, 1, 1, 7, 36, 135, 344, 510, 295, 1, 1, 8, 49, 231, 805, 1908, 2602, 1329, 1, 1, 9, 64, 364, 1616, 5325, 11904, 15133, 6934, 1, 1, 10, 81, 540, 2919, 12381, 39001, 83028, 99367, 41351, 1

Offset: 0

Author

Paul D. Hanna, Sep 07 2004

Keywords

• nonn
• tabl

Comments

The rows of this triangle are the reverse of the rows of triangle A091351, in which the k-th column lists the row sums of the k-th matrix power of A091351. Row sums form A091352 and equal the secondary diagonal.

Examples

			T(7,3) = T(3,0)*T(6,3) + T(3,1)*T(5,2) + T(3,2)*T(4,1) + T(3,3)*T(3,0)
= 1*70 + 3*16 + 4*4 + 1*1 = 135.
Rows begin:
[1],
[1,1],
[1,2,1],
[1,3,4,1],
[1,4,9,9,1],
[1,5,16,30,24,1],
[1,6,25,70,115,77,1],
[1,7,36,135,344,510,295,1],
[1,8,49,231,805,1908,2602,1329,1],
[1,9,64,364,1616,5325,11904,15133,6934,1],...
		

Crossrefs

Cf. A091351, A091352.

Programs

PARI

T(n,k)=if(n
				

Formula

T(n, k) = Sum_{i=0..k} T(k, i)*T(n-i-1, k-i) for 0

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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