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A265144 Number of lambda-parking functions of the unique partition lambda with encoding n = Product_{i:lambda} prime(i).

%I A265144 #17 Aug 21 2021 05:18:30
%S A265144 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,
%T A265144 1,16,13,15,11,12,15,20,9,13,25,14,13,20,17,15,6,16,19,24,16,16,15,21,
%U A265144 13,28,19,17,27,18,21,32,1,27,34,19,19,32,34,20,16
%N A265144 Number of lambda-parking functions of the unique partition lambda with encoding n = Product_{i:lambda} prime(i).
%H A265144 Alois P. Heinz, <a href="/A265144/b265144.txt">Table of n, a(n) for n = 1..20000</a>
%H A265144 Richard P. Stanley, <a href="http://math.mit.edu/~rstan/transparencies/parking.pdf">Parking Functions</a>, 2011.
%e A265144 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.
%p A265144 with(numtheory):
%p A265144 p:= l-> (n-> n!*LinearAlgebra[Determinant](Matrix(n, (i, j)
%p A265144          -> (t->`if`(t<0, 0, l[i]^t/t!))(j-i+1))))(nops(l)):
%p A265144 a:= n-> p(sort([seq(pi(i[1])$i[2], i=ifactors(n)[2])])):
%p A265144 seq(a(n), n=1..100);
%t A265144 p[l_] := Function[n, n! Det[Table[Function[t, If[t<0, 0,
%t A265144      l[[i]]^t/t!]][j-i+1], {i, n}, {j, n}]]][Length[l]];
%t A265144 a[n_] := If[n==1, 1, p[Sort[Flatten[Table[Table[
%t A265144      PrimePi[i[[1]]], {i[[2]]}], {i, FactorInteger[n]}]]]]];
%t A265144 Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Aug 21 2021, after _Alois P. Heinz_ *)
%Y A265144 Cf. A000040, A000041, A215366, A265145.
%K A265144 nonn,look
%O A265144 1,3
%A A265144 _Alois P. Heinz_, Dec 02 2015