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A265016 Total sum of number of lambda-parking functions, where lambda ranges over all partitions of n into distinct parts. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..100

Richard P. Stanley, Parking Functions, 2011.

EXAMPLE

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.

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<n, 0, `if`(n=0, p(l),

    g(n, i-1, l)+`if`(i>n, 0, g(n-i, i-1, [i, l[]])))):

a:= n-> g(n$2, []):

seq(a(n), n=0..35);

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-Fran├žois Alcover, Aug 20 2021, after Alois P. Heinz *)

CROSSREFS

Row sums of A265017, A265018, A265019, A265020.

Cf. A000009, A265007, A265202.

Sequence in context: A325040 A350949 A088902 * A279897 A336131 A095967

Adjacent sequences:  A265013 A265014 A265015 * A265017 A265018 A265019

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 30 2015

STATUS

approved

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Last modified May 21 21:43 EDT 2022. Contains 353929 sequences. (Running on oeis4.)