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A329059
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3-parking triangle T(r, i, 3) read by rows: T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i) with k = 3 and 0 <= i <= r.
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5
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1, 3, 1, 15, 9, 3, 91, 78, 48, 16, 612, 680, 600, 375, 125, 4389, 5985, 6840, 6156, 3888, 1296, 32890, 53130, 74382, 86779, 79233, 50421, 16807, 254475, 475020, 786240, 1123200, 1331200, 1228800, 786432, 262144, 2017356, 4272048, 8155728, 13762791, 19978245, 23973894, 22320522, 14348907, 4782969
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OFFSET
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0,2
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COMMENTS
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The k-parking numbers interpolate between the generalized Fuss-Catalan numbers and the number of parking functions (see Yip).
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LINKS
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FORMULA
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T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i).
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EXAMPLE
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r/i| 0 1 2 3 4
———————————————————————————————————————
0 | 1
1 | 3 1
2 | 15 9 3
3 | 91 78 48 16
4 | 612 680 600 375 125
...
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MATHEMATICA
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T[r_, i_, k_] := (r + 1)^(i-1)*Binomial[k*(r + 1) + r - i - 1, r - i]; Flatten[Table[T[r, i, 3], {r, 0, 8}, {i, 0, r}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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