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 A329057 1-parking triangle T(r, i, 1) read by rows: T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i) with k = 1 and 0 <= i <= r. 6
 1, 1, 1, 2, 3, 3, 5, 10, 16, 16, 14, 35, 75, 125, 125, 42, 126, 336, 756, 1296, 1296, 132, 462, 1470, 4116, 9604, 16807, 16807, 429, 1716, 6336, 21120, 61440, 147456, 262144, 262144, 1430, 6435, 27027, 104247, 360855, 1082565, 2657205, 4782969, 4782969, 4862, 24310, 114400, 500500, 2002000, 7150000, 22000000, 55000000, 100000000, 100000000 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The k-parking numbers interpolate between the generalized Fuss-Catalan numbers and the number of parking functions (see Yip). LINKS Stefano Spezia, First 151 rows of the triangle, flattened Carolina Benedetti, Rafael S. González D’León, Christopher R. H. Hanusa, Pamela E. Harris, Apoorva Khare, Alejandro H. Morales, Martha Yip, The volume of the caracol polytope, Séminaire Lotharingien de Combinatoire 80B.87 (2018). 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, 1) = A000108(r). T(r, r, 1) = A000272(r + 1). EXAMPLE r/i|  0   1   2   3   4 ——————————————————————— 0  |  1 1  |  1   1 2  |  2   3   3 3  |  5  10  16  16 4  | 14  35  75 125 125 MATHEMATICA T[r_, i_, k_] := (r + 1)^(i-1)*Binomial[k*(r + 1) + r - i - 1, r - i]; Flatten[Table[T[r, i, 1], {r, 0, 9}, {i, 0, r}]] CROSSREFS Cf. A000108, A000272, A007318, A329058, A329059, A329060, A329096 (row sums). Sequence in context: A296674 A297073 A019460 * A236165 A049855 A286868 Adjacent sequences:  A329054 A329055 A329056 * A329058 A329059 A329060 KEYWORD nonn,tabl AUTHOR Stefano Spezia, Nov 02 2019 STATUS approved

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Last modified June 18 20:45 EDT 2021. Contains 345121 sequences. (Running on oeis4.)