A265016 Total sum of number of lambda-parking functions, where lambda ranges over all partitions of n into distinct parts.
1, 1, 2, 6, 9, 20, 43, 74, 130, 241, 493, 774, 1413, 2286, 3987, 7287, 11650, 19235, 31581, 50852, 80867, 141615, 214538, 349179, 541603, 859759, 1303221, 2054700, 3277493, 4960397, 7652897, 11662457, 17703655, 26603187, 40043433, 59384901, 92234897, 134538472
Offset: 0
Keywords
Examples
The number of lambda-parking functions induced by the partitions of 4 into distinct parts: 5 by [1,3]: [1,1], [1,2], [2,1], [1,3], [3,1], 4 by [4]: [1], [2], [3], [4]. a(4) = 5 + 4 = 9.
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..100
- Richard P. Stanley, Parking Functions, 2011.
Programs
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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)): g:= (n, i, l)-> `if`(i*(i+1)/2 -
Mathematica
p[l_] := With[{n = Length[l]}, n!*Det[Table[Function[t, If[t < 0, 0, l[[i]]^t/t!]][j - i + 1], {i, n}, {j, n}]]]; g[n_, i_, l_] := If[i (i + 1)/2 < n, 0, If[n == 0, p[l], g[n, i - 1, l] + If[i > n, 0, g[n - i, i - 1, Prepend[l, i]]]]]; a[n_] := If[n == 0, 1, g[n, n, {}]]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Aug 20 2021, after Alois P. Heinz *)