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.

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

Author

Stefano Spezia, Nov 02 2019

Keywords

• nonn
• tabl

Comments

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

Examples

			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
		

Links

• Stefano Spezia, First 151 rows of the triangle, flattened
• Martha Yip, A Fuss-Catalan variation of the caracol flow polytope, arXiv:1910.10060 [math.CO], 2019.

Crossrefs

Cf. A000108, A000272, A006013, A007318, A329057, A329059, A329060, A329113 (row sums).

Programs

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}]]

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).