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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, 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
0,5
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.
FORMULA
T(n, k) = Sum_{i=0..k} T(k, i)*T(n-i-1, k-i) for 0<k<n, else T(0, n)=T(n, n)=1.
EXAMPLE
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],...
PROG
(PARI) T(n, k)=if(n<k || k<0, 0, if(n==k || k==0, 1, sum(i=0, k, T(k, i)*T(n-i-1, k-i)); ))
CROSSREFS
Sequence in context: A009999 A322268 A144823 * A098447 A202784 A175105
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Sep 07 2004
STATUS
approved