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A298597 Number T(n,k) of times the value k appears on the parking functions of length n and such that if we replace that value k with k+1 we don't get a parking function. 3
1, 2, 2, 9, 6, 9, 64, 36, 36, 64, 625, 320, 270, 320, 625, 7776, 3750, 2880, 2880, 3750, 7776, 117649, 54432, 39375, 35840, 39375, 54432, 117649, 2097152, 941192, 653184, 560000, 560000, 653184, 941192, 2097152, 43046721, 18874368, 12706092, 10450944, 9843750, 10450944, 12706092, 18874368, 43046721 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..45.

FORMULA

T(n,k) = n*binomial(n-1, k-1)*k^(k-2)*(n+1-k)^(n-1-k).

T(n,k) = n*A298594(n,k).

T(n.k) = A298593(n,k)-A298593(n,k+1).

T(n,k) = n*(A298592(n,k)-A298592(n,k+1)).

T(n,1) = n*A000272(n+2).

T(n,n) = n*A000272(n+2).

T(n,1) = A000169(n).

T(n,n) = A000169(n).

T(n,k) = T(n,n-k).

EXAMPLE

Triangle begins:

        1;

        2,      2;

        9,      6,      9;

       64,     36,     36,     64;

      625,    320,    270,    320,    625;

     7776,   3750,   2880,   2880,   3750,   7776;

   117649,  54432,  39375,  35840,  39375,  54432, 117649;

  2097152, 941192, 653184, 560000, 560000, 653184, 941192, 2097152;

  ...

MATHEMATICA

Table[n Binomial[n - 1, k - 1] k^(k - 2)*(n + 1 - k)^(n - 1 - k), {n, 9}, {k, n}] // Flatten (* Michael De Vlieger, Jan 22 2018 *)

CROSSREFS

Cf. A000169, A000272, A298592, A298593, A298594.

Sequence in context: A093589 A319129 A073315 * A066320 A005168 A256591

Adjacent sequences:  A298594 A298595 A298596 * A298598 A298599 A298600

KEYWORD

easy,nonn,tabl

AUTHOR

Rui Duarte, Jan 22 2018

STATUS

approved

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Last modified April 16 12:45 EDT 2021. Contains 343037 sequences. (Running on oeis4.)