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 A333829 Triangle read by rows: T(n,k) is the number of parking functions of length n with k strict descents. T(n,k) for n >= 1 and 0 <= k <= n-1. 1
 1, 2, 1, 5, 10, 1, 14, 73, 37, 1, 42, 476, 651, 126, 1, 132, 2952, 8530, 4770, 422, 1, 429, 17886, 95943, 114612, 31851, 1422, 1, 1430, 107305, 987261, 2162033, 1317133, 202953, 4853, 1, 4862, 642070, 9613054, 35196634, 39471355, 13792438, 1262800, 16786, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS In a parking function w(1), ..., w(n), a strict descent is an index i such that w(i) > w(i+1). Define an n-dimensional polytope as the convex hull of length n+1 nondecreasing parking functions. Then, the Ehrhart h*-polynomial of this polytope is Sum_{k=0..n-1} T(n,k) * z^(n-1-k). LINKS Table of n, a(n) for n=1..45. Paul R. F. Schumacher, Descents in Parking Functions, J. Int. Seq. 21 (2018), #18.2.3. EXAMPLE The triangle T(n,k) begins: n/k 0 1 2 3 4 5 1 1 2 2 1 3 5 10 1 4 14 73 37 1 5 42 476 651 126 1 6 132 2952 8530 4770 422 1 ... The 10 parking functions of length 3 with 1 strict descent are: [[1, 2, 1], [2, 1, 1], [1, 3, 1], [3, 1, 1], [2, 1, 2], [2, 2, 1], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2]]. PROG (SageMath) var('z, t') assume(0

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Last modified December 4 10:52 EST 2023. Contains 367560 sequences. (Running on oeis4.)