A152543 -id:A152543

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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.

+10
3

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

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

EXAMPLE

Triangle begins:

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.

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Dec 12 2008

STATUS

approved

A152542

Column 0 of triangle A152541.

+10
3

1, 2, 16, 230, 4704, 124388, 4029888, 154462924, 6834212520, 342732052968, 19208758459008, 1189732051180016, 80692431912452864, 5947714658316493728, 473385135814528562176, 40461455930940173038416

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..15.

CROSSREFS

Cf. A152541, A152543, A152544.

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 12 2008

STATUS

approved

A152544

Column 2 of triangle A152541.

+10
3

3, 12, 128, 2162, 49600, 1432844, 49817952, 2023012156, 93912730296, 4904242685400, 284505673264128, 18151332186337616, 1263090275990339328, 95206191201187298144, 7727681258907211662080, 672032111511007152558288

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

Table of n, a(n) for n=0..15.

CROSSREFS

Cf. A152541, A152542, A152543.

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 12 2008

STATUS

approved

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