%I #10 Nov 06 2019 10:26:32

%S 1,3,1,15,9,3,91,78,48,16,612,680,600,375,125,4389,5985,6840,6156,

%T 3888,1296,32890,53130,74382,86779,79233,50421,16807,254475,475020,

%U 786240,1123200,1331200,1228800,786432,262144,2017356,4272048,8155728,13762791,19978245,23973894,22320522,14348907,4782969

%N 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 The k-parking numbers interpolate between the generalized Fuss-Catalan numbers and the number of parking functions (see Yip).

%H Stefano Spezia, <a href="/A329059/b329059.txt">First 151 rows of the triangle, flattened</a>

%H 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 T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i).

%F T(r, 0, 3) = A006632(r + 1).

%F T(r, r, 3) = A000272(r + 1).

%e r/i| 0 1 2 3 4

%e ———————————————————————————————————————

%e 0 | 1

%e 1 | 3 1

%e 2 | 15 9 3

%e 3 | 91 78 48 16

%e 4 | 612 680 600 375 125

%e ...

%t 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 Cf. A000108, A000272, A006632, A007318, A328978 (row sums), A329057, A329058, A329060.

%K nonn,tabl

%O 0,2

%A _Stefano Spezia_, Nov 03 2019