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A374738 Table read by ascending antidiagonals: T(m,n) = number of (n-1)-metered (m,n)-parking functions.

%I A374738 #11 Jul 18 2024 14:27:06
%S A374738 1,1,2,1,3,3,1,4,8,4,1,6,16,15,5,1,8,27,50,24,6,1,12,48,125,108,35,7,
%T A374738 1,16,96,257,432,196,48,8,1,24,162,540,1296,1029,320,63,9,1,32,288,
%U A374738 1200,3156,4802,2048,486,80,10,1,48,576,3000,7734,16807,12288,3645,700,99,11
%N A374738 Table read by ascending antidiagonals: T(m,n) = number of (n-1)-metered (m,n)-parking functions.
%H A374738 Spencer Daugherty, Pamela E. Harris, Ian Klein, and Matt McClinton, <a href="https://arxiv.org/abs/2406.12941">Metered Parking Functions</a>, arXiv:2406.12941 [math.CO], 2024.
%F A374738 T(n+k,n) = Sum_{sigma = (sigma_1, ..., sigma_n) in S_n} (( Product_{i=1..n} L_{i}(sigma))( Product_{j=1..k} sigma_j mod n )), where k>0 and L_{i}(sigma) is the largest index h with i<h for which sigma_i >= sigma_N for all N in {i-j, i-j+1, ..., i-1, i}.
%e A374738 Table begins:
%e A374738    1,  2,   3,    4,    5,     6,      7, ...
%e A374738    1,  3,   8,   15,   24,    35,     48, ...
%e A374738    1,  4,  16,   50,  108,   196,    320, ...
%e A374738    1,  6,  27,  125,  432,  1029,   2048, ...
%e A374738    1,  8,  48,  257, 1296,  4802,  12288, ...
%e A374738    1, 12,  96,  540, 3156, 16807,  65536, ...
%e A374738    1, 16, 162, 1200, 7734, 47442, 262144, ...
%e A374738    ...
%Y A374738 The n=m+1 diagonal is A007334.
%Y A374738 Cf. A372817, A372818, A372819, A372820, A372821.
%K A374738 nonn,tabl
%O A374738 1,3
%A A374738 _Spencer Daugherty_, Jul 18 2024