A128567 Matrix square, T(n,k), of Parker's partition triangle A047812, read by rows (n >= 1 and 0 <= k <= n-1).
1, 2, 1, 5, 6, 1, 14, 31, 14, 1, 42, 133, 117, 22, 1, 132, 587, 813, 300, 36, 1, 429, 2531, 4871, 2896, 692, 52, 1, 1430, 10950, 27743, 23961, 9206, 1430, 76, 1, 4862, 47185, 151208, 175734, 96418, 24598, 2798, 104, 1, 16796, 203704, 804065, 1200301, 882471, 329426, 62885, 5236, 146, 1
Offset: 1
Examples
Triangle T(n,k) (with rows n >= 1 and columns k = 0..n-1) begins:
1;
2, 1;
5, 6, 1;
14, 31, 14, 1;
42, 133, 117, 22, 1;
132, 587, 813, 300, 36, 1;
429, 2531, 4871, 2896, 692, 52, 1;
1430, 10950, 27743, 23961, 9206, 1430, 76, 1;
4862, 47185, 151208, 175734, 96418, 24598, 2798, 104, 1;
16796, 203704, 804065, 1200301, 882471, 329426, 62885, 5236, 146, 1;
...
Links
- R. K. Guy, Parker's permutation problem involves the Catalan numbers, preprint, 1992. (Annotated scanned copy)
- R. K. Guy, Parker's permutation problem involves the Catalan numbers, Amer. Math. Monthly 100 (1993), 287-289.
- Wikipedia, E. T. Parker.
Crossrefs
Programs
-
PARI
{T(n, k)=local(M);M=matrix(n+1,n+1,r,c,if(r
Formula
T(n,k) = Sum_{s=k..n-1} A047812(n,s)*A047812(s+1,k) for n >= 1 and 0 <= k <= n-1. - Petros Hadjicostas, May 31 2020
Extensions
Name edited and offset changed by Petros Hadjicostas, May 30 2020
Comments