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A329058
2-parking triangle T(r, i, 2) read by rows: T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i) with k = 2 and 0 <= i <= r.
5
1, 2, 1, 7, 6, 3, 30, 36, 32, 16, 143, 220, 275, 250, 125, 728, 1365, 2184, 2808, 2592, 1296, 3876, 8568, 16660, 27440, 36015, 33614, 16807, 21318, 54264, 124032, 248064, 417792, 557056, 524288, 262144, 120175, 346104, 908523, 2133054, 4363065, 7479540, 10097379, 9565938, 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, 2) = A006013(r).
T(r, r, 2) = A000272(r + 1).
EXAMPLE
r/i| 0 1 2 3 4
————————————————————————
0 | 1
1 | 2 1
2 | 7 6 3
3 | 30 36 32 16
4 | 143 220 275 250 125
MATHEMATICA
T[r_, i_, k_] := (r + 1)^(i-1)*Binomial[k*(r + 1) + r - i - 1, r - i]; Flatten[Table[T[r, i, 2], {r, 0, 9}, {i, 0, r}]]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, Nov 02 2019
STATUS
approved