A265202 Total number of lambda-parking functions induced by all partitions of n into distinct parts.

1, 1, 2, 6, 9, 15, 36, 53, 78, 119, 286, 401, 591, 829, 1232, 2910, 4084, 5789, 8070, 11281, 15823, 37747, 51622, 72919, 98986, 136600, 181648, 254638, 586891, 799841, 1110303, 1495279, 2018749, 2657612, 3552560, 4738775, 10857521, 14560375, 20061359, 26603227

Offset: 0

Author

Alois P. Heinz, Dec 04 2015

Keywords

• nonn

Examples

			a(0) = 1: [].
a(1) = 1: [1].
a(2) = 2: [1], [2].
a(3) = 6: [1], [2], [3], [1,1], [1,2], [2,1].
a(4) = 9: [1], [2], [3], [4], [1,1], [1,2], [1,3], [2,1], [3,1].
a(5) = 15: [1], [2], [3], [4], [5], [1,1], [1,2], [1,3], [1,4], [2,1], [2,2], [2,3], [3,1], [3,2], [4,1].
a(6) = 36: [1], [2], [3], [4], [5], [6], [1,1], [1,2], [1,3], [1,4], [1,5], [2,1], [2,2], [2,3], [2,4], [3,1], [3,2], [4,1], [4,2], [5,1], [1,1,1], [1,1,2], [1,1,3], [1,2,1], [1,2,2], [1,2,3], [1,3,1], [1,3,2], [2,1,1], [2,1,2], [2,1,3], [2,2,1], [2,3,1], [3,1,1], [3,1,2], [3,2,1].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400
• Richard P. Stanley, Parking Functions, 2011

Crossrefs

Row sums of A265208.

Cf. A000009, A255047, A265016.

Programs

Maple

b:= proc(p, g, n, i, t) option remember; `if`(g=0, 0, p!/g!)+
      `if`(n `if`(n=0, 1, b(0$2, n, 1$2)):
seq(a(n), n=0..50);

Mathematica

b[p_, g_, n_, i_, t_] := b[p, g, n, i, t] = If[g==0, 0, p!/g!] + If[nJean-François Alcover, Feb 02 2017, translated from Maple *)