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A265144 Number of lambda-parking functions of the unique partition lambda with encoding n = Product_{i:lambda} prime(i). 2
1, 1, 2, 1, 3, 3, 4, 1, 4, 5, 5, 4, 6, 7, 8, 1, 7, 7, 8, 7, 12, 9, 9, 5, 9, 11, 8, 10, 10, 16, 11, 1, 16, 13, 15, 11, 12, 15, 20, 9, 13, 25, 14, 13, 20, 17, 15, 6, 16, 19, 24, 16, 16, 15, 21, 13, 28, 19, 17, 27, 18, 21, 32, 1, 27, 34, 19, 19, 32, 34, 20, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..20000

R. Stanley, Parking Functions, 2011

EXAMPLE

n = 18 = 2*3*3 = prime(1)*prime(2)*prime(2) encodes partition [1,2,2] having seven lambda-parking functions: [1,1,1], [1,1,2], [1,2,1], [2,1,1], [1,2,2], [2,1,2], [2,2,1], thus a(18) = 7.

MAPLE

with(numtheory):

p:= l-> (n-> n!*LinearAlgebra[Determinant](Matrix(n, (i, j)

         -> (t->`if`(t<0, 0, l[i]^t/t!))(j-i+1))))(nops(l)):

a:= n-> p(sort([seq(pi(i[1])$i[2], i=ifactors(n)[2])])):

seq(a(n), n=1..100);

CROSSREFS

Cf. A000040, A000041, A215366, A265145.

Sequence in context: A066328 A319225 A304037 * A263275 A308057 A097686

Adjacent sequences:  A265141 A265142 A265143 * A265145 A265146 A265147

KEYWORD

nonn,look

AUTHOR

Alois P. Heinz, Dec 02 2015

STATUS

approved

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Last modified September 16 12:28 EDT 2019. Contains 327098 sequences. (Running on oeis4.)