OFFSET
0,5
LINKS
Seiichi Manyama, Rows n = 0..139, flattened
E. Ackerman, G. Barequet, R. Y. Pinter and D. Romik, The number of guillotine partitions in d dimensions, Inf. Proc. Lett 98 (4) (2006) 162-167.
FORMULA
Number triangle T(n, k)=if(k<=n, sum{j=0..k, C(k+j, 2j)(n-k)^j*C(j)}, 0), C(n) given by A000108.
EXAMPLE
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 3, 6, 1;
1, 4, 15, 22, 1;
1, 5, 28, 93, 90, 1;
1, 6, 45, 244, 645, 394, 1;
1, 7, 66, 505, 2380, 4791, 1806, 1;
1, 8, 91, 906, 6345, 24868, 37275, 8558, 1;
...
PROG
(PARI) T(n, k) = sum(j=0, k, (n-k)^j*binomial(k+j, 2*j)*binomial(2*j, j)/(j+1)); \\ Seiichi Manyama, Oct 02 2023
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, May 21 2005
STATUS
approved