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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.
5
1, 4, 1, 26, 12, 3, 204, 136, 64, 16, 1771, 1540, 1050, 500, 125, 16380, 17550, 15600, 10800, 5184, 1296, 158224, 201376, 220255, 198940, 139258, 67228, 16807, 1577532, 2324784, 3015936, 3351040, 3063808, 2162688, 1048576, 262144, 16112057, 26978328, 40467492, 53298648, 59960979, 55348596, 39326634, 19131876, 4782969
OFFSET
0,2
COMMENTS
The k-parking numbers interpolate between the generalized Fuss-Catalan numbers and the number of parking functions (see Yip).
LINKS
Martha Yip, A Fuss-Catalan variation of the caracol flow polytope, arXiv:1910.10060 [math.CO], 2019.
FORMULA
T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i).
T(r, 0, 4) = A118971(r).
T(r, r, 4) = A000272(r + 1).
EXAMPLE
r/i| 0 1 2 3 4
—————————————————————————————————————
0 | 1
1 | 4 1
2 | 26 12 3
3 | 204 136 64 16
4 | 1771 1540 1050 500 125
...
MATHEMATICA
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}]]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, Nov 03 2019
STATUS
approved