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A333062 Number of entries in the fifth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths. 2
1, 16, 162, 1345, 10096, 72973, 531015, 3984762, 30987321, 248303940, 2036778980, 17044330217, 145588640408, 1272940217747, 11434350878640, 105849240653792, 1011701166471075, 9987958951272492, 101765834737586068, 1068365602976497915, 11534318293877771406 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 5..576

Wikipedia, Partition of a set

MAPLE

b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,

      add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(

       combinat[multinomial](n, i$j, n-i*j)/j!*

      b(n-i*j, min(n-i*j, i-1), max(0, t-j))), j=0..n/i)))

    end:

a:= n-> b(n$2, 5)[2]:

seq(a(n), n=5..25);

MATHEMATICA

multinomial[n_, k_List] := n!/Times @@ (k!);

b[n_, i_, t_] := b[n, i, t] = If[n == 0, {1, 0}, If[i < 1, {0, 0}, Sum[

     Function[p, p + If[t > 0 && t - j < 1, {0, p[[1]]*i}, {0, 0}]][

     multinomial[n, Append[Table[i, {j}], n - i*j]]/j!*

     b[n - i*j, Min[n - i*j, i - 1], Max[0, t - j]]], {j, 0, n/i}]]];

a[n_] := b[n, n, 5][[2]];

a /@ Range[5, 25] (* Jean-François Alcover, Apr 24 2021, after Alois P. Heinz *)

CROSSREFS

Column k=5 of A319375.

Sequence in context: A085538 A259547 A211558 * A208311 A232333 A091363

Adjacent sequences:  A333059 A333060 A333061 * A333063 A333064 A333065

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 06 2020

STATUS

approved

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Last modified October 17 00:35 EDT 2021. Contains 348048 sequences. (Running on oeis4.)