A298594 - OEIS

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A298594

Triangle read by rows: T(n,k) = number of parking functions a of length n such that a(1) = k and if we replace a(1) = k with k+1 we don't get a parking function.

1, 1, 1, 3, 2, 3, 16, 9, 9, 16, 125, 64, 54, 64, 125, 1296, 625, 480, 480, 625, 1296, 16807, 7776, 5625, 5120, 5625, 7776, 16807, 262144, 117649, 81648, 70000, 70000, 81648, 117649, 262144, 4782969, 2097152, 1411788, 1161216, 1093750, 1161216, 1411788, 2097152, 4782969

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,4

LINKS

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

FORMULA

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

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

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

T(n,k) = A298597(n,k)/n.

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

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

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

EXAMPLE

Triangle begins:

1, 1;

3, 2, 3;

16, 9, 9, 16;

125, 64, 54, 64, 125;

1296, 625, 480, 480, 625, 1296;

16807, 7776, 5625, 5120, 5625, 7776, 16807;

262144, 117649, 81648, 70000, 70000, 81648, 117649, 262144;

...

MATHEMATICA

Table[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. A000272, A298592, A298593, A298597.

Sequence in context: A081850 A247237 A059366 * A092950 A059239 A350517

Adjacent sequences: A298591 A298592 A298593 * A298595 A298596 A298597

KEYWORD

easy,nonn,tabl

AUTHOR

Rui Duarte, Jan 22 2018

STATUS

approved