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A329059 3-parking triangle T(r, i, 3) read by rows: T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i) with k = 3 and 0 <= i <= r.

%I A329059 #10 Nov 06 2019 10:26:32
%S A329059 1,3,1,15,9,3,91,78,48,16,612,680,600,375,125,4389,5985,6840,6156,
%T A329059 3888,1296,32890,53130,74382,86779,79233,50421,16807,254475,475020,
%U A329059 786240,1123200,1331200,1228800,786432,262144,2017356,4272048,8155728,13762791,19978245,23973894,22320522,14348907,4782969
%N A329059 3-parking triangle T(r, i, 3) read by rows: T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i) with k = 3 and 0 <= i <= r.
%C A329059 The k-parking numbers interpolate between the generalized Fuss-Catalan numbers and the number of parking functions (see Yip).
%H A329059 Stefano Spezia, <a href="/A329059/b329059.txt">First 151 rows of the triangle, flattened</a>
%H A329059 Martha Yip, <a href="https://arxiv.org/abs/1910.10060">A Fuss-Catalan variation of the caracol flow polytope</a>, arXiv:1910.10060 [math.CO], 2019.
%F A329059 T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i).
%F A329059 T(r, 0, 3) = A006632(r + 1).
%F A329059 T(r, r, 3) = A000272(r + 1).
%e A329059 r/i|      0      1      2      3      4
%e A329059 ———————————————————————————————————————
%e A329059 0  |      1
%e A329059 1  |      3      1
%e A329059 2  |     15      9      3
%e A329059 3  |     91     78     48     16
%e A329059 4  |    612    680    600    375    125
%e A329059 ...
%t A329059 T[r_, i_,k_] := (r + 1)^(i-1)*Binomial[k*(r + 1) + r - i - 1, r - i]; Flatten[Table[T[r,i,3],{r,0,8},{i,0,r}]]
%Y A329059 Cf. A000108, A000272, A006632, A007318, A328978 (row sums), A329057, A329058, A329060.
%K A329059 nonn,tabl
%O A329059 0,2
%A A329059 _Stefano Spezia_, Nov 03 2019