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A271735
Number of set partitions of [n] with maximal block length multiplicity equal to six.
2
1, 0, 28, 84, 840, 5082, 48279, 413127, 3093090, 26601575, 255431176, 2309491548, 20998179748, 209051155600, 2137087555220, 21652990622410, 230200208290745, 2517313465793819, 28104615964752327, 320432370881428575, 3760667223506993800, 45094960570293757695
OFFSET
6,3
COMMENTS
At least one block length occurs exactly 6 times, and all block lengths occur at most 6 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, 6)-b(n$2, 5):
seq(a(n), n=6..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, 6] - b[n, n, 5];
Table[a[n], {n, 6, 30}] (* Jean-François Alcover, May 08 2018, after Alois P. Heinz *)
CROSSREFS
Column k=6 of A271423.
Sequence in context: A179790 A306427 A254145 * A280885 A042542 A042540
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 13 2016
STATUS
approved