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A265145 Number of lambda-parking functions of the unique strict partition lambda with parts i_1<i_2<...<i_m and encoding n = Product_{j=1..m} prime(i_j-j+1). 4
1, 1, 2, 3, 3, 5, 4, 16, 8, 7, 5, 25, 6, 9, 12, 125, 7, 34, 8, 34, 16, 11, 9, 189, 15, 13, 50, 43, 10, 49, 11, 1296, 20, 15, 21, 243, 12, 17, 24, 253, 13, 64, 14, 52, 74, 19, 15, 1921, 24, 58, 28, 61, 16, 307, 27, 317, 32, 21, 17, 343, 18, 23, 98, 16807, 33 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A strict partition is a partition into distinct parts.

LINKS

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

R. Stanley, Parking Functions, 2011

EXAMPLE

n = 10 = 2*5 = prime(1)*prime(3) encodes strict partition [1,4] having seven lambda-parking functions: [1,1], [1,2], [2,1], [1,3], [3,1], [1,4], [4,1], thus a(10) = 7.

MAPLE

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((l-> [seq(l[j]+j-1, j=1..nops(l))])(sort([seq(

         numtheory[pi](i[1])$i[2], i=ifactors(n)[2])]))):

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

CROSSREFS

Cf. A000009, A000040, A265144, A265146, A265208.

Sequence in context: A238792 A158745 A175108 * A103310 A046146 A081768

Adjacent sequences:  A265142 A265143 A265144 * A265146 A265147 A265148

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 02 2015

STATUS

approved

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Last modified April 7 13:27 EDT 2020. Contains 333305 sequences. (Running on oeis4.)