A152798 Triangle defined by T(n,k) = Sum_{j=0..k} C(k,j)*T(n-1,j+k) for n>k>0 with T(n,0)=T(n,n)=1, read by rows.

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 6, 6, 4, 1, 1, 1, 12, 15, 10, 5, 1, 1, 1, 27, 40, 29, 15, 6, 1, 1, 1, 67, 113, 93, 49, 21, 7, 1, 1, 1, 180, 348, 310, 180, 76, 28, 8, 1, 1, 1, 528, 1148, 1106, 685, 311, 111, 36, 9, 1, 1, 1, 1676, 4045, 4205, 2748, 1322, 497, 155, 45

Offset: 0

Author

Paul D. Hanna, Dec 23 2008

Keywords

• nonn
• tabl

Examples

			Triangle begins:
1;
1, 1;
1, 1, 1;
1, 2, 1, 1;
1, 3, 3, 1, 1;
1, 6, 6, 4, 1, 1;
1, 12, 15, 10, 5, 1, 1;
1, 27, 40, 29, 15, 6, 1, 1;
1, 67, 113, 93, 49, 21, 7, 1, 1;
1, 180, 348, 310, 180, 76, 28, 8, 1, 1;
1, 528, 1148, 1106, 685, 311, 111, 36, 9, 1, 1;
1, 1676, 4045, 4205, 2748, 1322, 497, 155, 45, 10, 1, 1;
1, 5721, 15203, 16912, 11683, 5858, 2323, 750, 209, 55, 11, 1, 1;
1, 20924, 60710, 71858, 52262, 27349, 11230, 3809, 1083, 274, 66, 12, 1, 1; ...
ILLUSTRATE RECURRENCE:
T(6,1) = T(5,1) + T(5,2) = 6 + 6 = 12;
T(7,2) = T(6,2) + 2*T(6,3) + T(6,4) = 6 + 2*4 + 1 = 15;
T(8,3) = T(7,3) + 3*T(7,4) + 3*T(7,5) + T(7,6) = 29 + 3*15 + 3*6 + 1 = 93.
Note that column 1 equals A122889: [1,1,2,3,6,12,27,67,180,528,...]
which is the antidiagonal sums of triangle A122888.
RELATED TRIANGLE A122888 begins:
1;
1, 1;
1, 2, 2, 1;
1, 3, 6, 9, 10, 8, 4, 1;
1, 4, 12, 30, 64, 118, 188, 258, 302, 298, 244, 162, 84, 32, 8, 1;
1, 5, 20, 70, 220, 630, 1656, 4014, 8994, 18654, 35832, 63750,...;
1, 6, 30, 135, 560, 2170, 7916, 27326, 89582, 279622, 832680,...;
1, 7, 42, 231, 1190, 5810, 27076, 121023, 520626, 2161158,...;
1, 8, 56, 364, 2240, 13188, 74760, 409836, 2179556, 11271436,...; ...
in which the g.f. of row n equals the n-th iteration of (x+x^2).
		

Crossrefs

Cf. A122888; columns: A122889, A152799; variant: A101494.

Programs

PARI

T(n, k)=if(n