A152541 Triangle, read by rows, where T(n,k) = Sum_{i=k..n-1} T(n-1,i)*T(i+1,k+1) for n>k with T(n,n) = n+1 for n>=0.

1, 2, 2, 16, 6, 3, 230, 54, 12, 4, 4704, 818, 128, 20, 5, 124388, 17360, 2162, 250, 30, 6, 4029888, 472484, 49600, 4742, 432, 42, 7, 154462924, 15666720, 1432844, 118920, 9158, 686, 56, 8, 6834212520, 612024124, 49817952, 3688268, 251216, 16130, 1024

Offset

0,2

Links

Table of n, a(n) for n=0..42.

Example

Triangle begins:
1;
2, 2;
16, 6, 3;
230, 54, 12, 4;
4704, 818, 128, 20, 5;
124388, 17360, 2162, 250, 30, 6;
4029888, 472484, 49600, 4742, 432, 42, 7;
154462924, 15666720, 1432844, 118920, 9158, 686, 56, 8;
6834212520, 612024124, 49817952, 3688268, 251216, 16130, 1024, 72, 9;
342732052968, 27510397296, 2023012156, 135928128, 8390756, 482464, 26498, 1458, 90, 10;
...
Illustrate the recurrence by row and column vector products:
T(3,0) = [16,6,3] * [2,6,54]~ = 16*2 + 6*6 + 3*54 = 230;
T(4,1) = [54,12,4] * [3,12,128]~ = 818;
T(4,0) = [230,54,12,4] * [2,6,54,818]~ = 4704.

Prog

(PARI) {T(n, k)=if(n==k, n+1, sum(i=k, n-1, T(n-1, i)*T(i+1, k+1)))}

Crossrefs

Cf. A152542, A152543, A152544.

Sequence in context: A097540 A345225 A112327 * A302339 A361817 A093114

Adjacent sequences: A152538 A152539 A152540 * A152542 A152543 A152544

Keyword

nonn,tabl

Author

Paul D. Hanna, Dec 12 2008

Status

approved