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 A370832 Triangle read by rows: T(n,k) gives the number of parking functions of size n with k lucky cars. 1 <= k <= n. 0
 1, 1, 2, 2, 8, 6, 6, 37, 58, 24, 24, 204, 504, 444, 120, 120, 1318, 4553, 6388, 3708, 720, 720, 9792, 44176, 87296, 81136, 33984, 5040, 5040, 82332, 463860, 1203921, 1582236, 1064124, 341136, 40320, 40320, 773280, 5270480, 17164320, 29724000, 28328480, 14602320, 3733920, 362880 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A car is called "lucky" if it gets its preferred parking spot. Closely related to A220884. LINKS Table of n, a(n) for n=1..45. Irfan Durmić, Alex Han, Pamela E. Harris, Rodrigo Ribeiro, and Mei Yin, Probabilistic Parking Functions, arXiv:2211.00536 [math.CO], 2022. FindStat, St000135: The number of lucky cars of the parking function. FORMULA T(n,n) = n!. T(n,1) = (n-1)!. Sum_{k=1..n} T(n,k) = (n+1)^(n-1). Conjecture: T(n,n-1) = A002538(n-1). Empirical g.f. for row n: Product_{j=2..n} x*(n + 1 + j*(x-1)). EXAMPLE Table begins: n\k| 1 2 3 4 5 6 7 8 ---+----------------------------------------------------------- 1 | 1 2 | 1 2 3 | 2 8 6 4 | 6 37 58 24 5 | 24 204 504 444 120 6 | 120 1318 4553 6388 3708 720 7 | 720 9792 44176 87296 81136 33984 5040 8 | 5040 82332 463860 1203921 1582236 1064124 341136 40320 CROSSREFS Cf. A002538, A067948, A220884. Sequence in context: A371937 A119999 A061828 * A086535 A344601 A067436 Adjacent sequences: A370828 A370830 A370831 * A370833 A370834 A370835 KEYWORD nonn,tabl AUTHOR Peter Kagey, Mar 02 2024 STATUS approved

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Last modified June 16 10:55 EDT 2024. Contains 373425 sequences. (Running on oeis4.)