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A329060 4-parking triangle T(r, i, 4) read by rows: T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i) with k = 4 and 0 <= i <= r.

%I A329060 #15 Jun 19 2025 09:19:34
%S A329060 1,4,1,26,12,3,204,136,64,16,1771,1540,1050,500,125,16380,17550,15600,
%T A329060 10800,5184,1296,158224,201376,220255,198940,139258,67228,16807,
%U A329060 1577532,2324784,3015936,3351040,3063808,2162688,1048576,262144,16112057,26978328,40467492,53298648,59960979,55348596,39326634,19131876,4782969
%N A329060 4-parking triangle T(r, i, 4) read by rows: T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i) with k = 4 and 0 <= i <= r.
%C A329060 The k-parking numbers interpolate between the generalized Fuss-Catalan numbers and the number of parking functions (see Yip).
%H A329060 Stefano Spezia, <a href="/A329060/b329060.txt">First 151 rows of the triangle, flattened</a>
%H A329060 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 A329060 T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i).
%F A329060 T(r, 0, 4) = A118971(r).
%F A329060 T(r, r, 4) = A000272(r + 1).
%e A329060 r/i|    0      1      2      3      4
%e A329060 —————————————————————————————————————
%e A329060 0  |    1
%e A329060 1  |    4      1
%e A329060 2  |   26     12      3
%e A329060 3  |  204    136     64     16
%e A329060 4  | 1771   1540   1050    500    125
%e A329060 ...
%t A329060 T[r_, i_, k_] := (r + 1)^(i-1)*Binomial[k*(r + 1) + r - i - 1, r - i]; Flatten[Table[T[r,i,4],{r,0,8},{i,0,r}]]
%Y A329060 Cf. A000108, A000272, A007318, A118971, A329057, A329058, A329059, A329123 (row sums).
%K A329060 nonn,tabl
%O A329060 0,2
%A A329060 _Stefano Spezia_, Nov 03 2019