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A298592 Triangle read by rows: T(n,k) = number of parking functions of length n whose lead number is k. 4
1, 2, 1, 8, 5, 3, 50, 34, 25, 16, 432, 307, 243, 189, 125, 4802, 3506, 2881, 2401, 1921, 1296, 65536, 48729, 40953, 35328, 30208, 24583, 16807, 1062882, 800738, 683089, 601441, 531441, 461441, 379793, 262144, 20000000, 15217031, 13119879, 11708091, 10546875, 9453125, 8291909, 6880121, 4782969 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

D. Foata and J. Riordan,  Mappings of acyclic and parking functions, J. Aeq. Math., 10 (1974) 10-22.

FORMULA

T(n,k) = Sum_{j=k..n} binomial(n-1, j-1)*j^(j-2)*(n+1-j)^(n-1-j).

T(n,k) = A298593(n,k)/n.

T(n,k) = Sum_{j=k..n} A298594(n,j).

T(n,k) = (Sum_{j=k..n} A298597(n,j))/n.

Sum_{k=1..n} T(n,k) = A000272(n+1).

EXAMPLE

Triangle begins:

        1;

        2,      1;

        8,      5,      3;

       50,     34,     25,     16;

      432,    307,    243,    189,    125;

     4802,   3506,   2881,   2401,   1921,   1296;

    65536,  48729,  40953,  35328,  30208,  24583,  16807;

  1062882, 800738, 683089, 601441, 531441, 461441, 379793, 262144;

  ...

MATHEMATICA

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

CROSSREFS

Cf. A000272, A298593, A298594, A298597.

Sequence in context: A136230 A193892 A193907 * A344163 A199468 A337684

Adjacent sequences:  A298589 A298590 A298591 * A298593 A298594 A298595

KEYWORD

easy,nonn,tabl

AUTHOR

Rui Duarte, Jan 22 2018

STATUS

approved

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Last modified June 23 17:34 EDT 2021. Contains 345402 sequences. (Running on oeis4.)