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A265202 Total number of lambda-parking functions induced by all partitions of n into distinct parts. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..400

R. Stanley, Parking Functions, 2011

EXAMPLE

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].

MAPLE

b:= proc(p, g, n, i, t) option remember; `if`(g=0, 0, p!/g!)+

      `if`(n<t, 0, add(b(p+1, `if`(i=j, g+1, 1), n-max(j, t), j,

       max(j+1, t+1))/`if`(i=j, 1, g!), j=i..n))

    end:

a:= 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[n<t, 0, Sum[b[p+1, If[i==j, g+1, 1], n-Max[j, t], j, Max[j+1, t+1]]/If[i==j, 1, g!], {j, i, n}]]; a[n_] := If[n==0, 1, b[0, 0, n, 1, 1]]; Table[a[n], {n, 0, 50}] (* Jean-Fran├žois Alcover, Feb 02 2017, translated from Maple *)

CROSSREFS

Row sums of A265208.

Cf. A000009, A255047, A265016.

Sequence in context: A103139 A181025 A345051 * A329743 A320496 A172433

Adjacent sequences:  A265199 A265200 A265201 * A265203 A265204 A265205

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 04 2015

STATUS

approved

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Last modified July 7 12:47 EDT 2022. Contains 355148 sequences. (Running on oeis4.)