%I #21 Aug 21 2021 05:19:32
%S 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,
%T 43,10,49,11,1296,20,15,21,243,12,17,24,253,13,64,14,52,74,19,15,1921,
%U 24,58,28,61,16,307,27,317,32,21,17,343,18,23,98,16807,33
%N 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).
%C A strict partition is a partition into distinct parts.
%H Alois P. Heinz, <a href="/A265145/b265145.txt">Table of n, a(n) for n = 1..20000</a>
%H Richard P. Stanley, <a href="http://math.mit.edu/~rstan/transparencies/parking.pdf">Parking Functions</a>, 2011.
%e 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.
%p p:= l-> (n-> n!*LinearAlgebra[Determinant](Matrix(n, (i, j)
%p -> (t->`if`(t<0, 0, l[i]^t/t!))(j-i+1))))(nops(l)):
%p a:= n-> p((l-> [seq(l[j]+j-1, j=1..nops(l))])(sort([seq(
%p numtheory[pi](i[1])$i[2], i=ifactors(n)[2])]))):
%p seq(a(n), n=1..100);
%t p[l_] := Function [n, n! Det[Table[Function[t, If[t<0, 0,
%t l[[i]]^t/t!]][j-i+1], {i, n}, {j, n}]]][Length[l]];
%t a[n_] := If[n==1, 1, p[Function[l, Flatten[Table[l[[j]]+j-1,
%t {j, 1, Length[l]}]]][Sort[Flatten[Table[Table[PrimePi[
%t i[[1]]], {i[[2]]}], {i, FactorInteger[n]}]]]]]];
%t Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Aug 21 2021, after _Alois P. Heinz_ *)
%Y Cf. A000009, A000040, A265144, A265146, A265208.
%K nonn
%O 1,3
%A _Alois P. Heinz_, Dec 02 2015