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A271734 Number of set partitions of [n] with maximal block length multiplicity equal to five. 2
1, 0, 21, 56, 504, 3717, 29337, 190674, 1460745, 12532520, 100025926, 845104624, 7657043576, 69364078980, 657324748866, 6374275533525, 64070264089020, 653567576544498, 6979149079277683, 74951288500334708, 835338959385664426, 9373747854520238761 (list; graph; refs; listen; history; text; internal format)
OFFSET
5,3
COMMENTS
At least one block length occurs exactly 5 times, and all block lengths occur at most 5 times.
LINKS
MAPLE
with(combinat):
b:= proc(n, i, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
*b(n-i*j, i-1, k)/j!, j=0..min(k, n/i))))
end:
a:= n-> b(n$2, 5)-b(n$2, 4):
seq(a(n), n=5..30);
MATHEMATICA
multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[multinomial[n, Join[{n - i*j}, Table[i, j]]]*b[n - i*j, i - 1, k]/j!, {j, 0, Min[k, n/i] }]]];
a[n_] := b[n, n, 5] - b[n, n, 4];
Table[a[n], {n, 5, 30}] (* Jean-François Alcover, May 08 2018, after Alois P. Heinz *)
CROSSREFS
Column k=5 of A271423.
Sequence in context: A067727 A254144 A165237 * A189004 A183310 A280884
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 13 2016
STATUS
approved

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Last modified May 23 02:40 EDT 2024. Contains 372758 sequences. (Running on oeis4.)