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A271737
Number of set partitions of [n] with maximal block length multiplicity equal to eight.
2
1, 0, 45, 165, 1980, 14157, 123123, 1042470, 11229075, 117721175, 1085614101, 11354532696, 132028149240, 1440550986525, 15693895739115, 183700174158435, 2200557929261230, 26295830857171150, 323510486572841425, 4085513198322259275, 52716487743732737925
OFFSET
8,3
COMMENTS
At least one block length occurs exactly 8 times, and all block lengths occur at most 8 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, 8)-b(n$2, 7):
seq(a(n), n=8..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, 8] - b[n, n, 7];
Table[a[n], {n, 8, 30}] (* Jean-François Alcover, May 08 2018, after Alois P. Heinz *)
CROSSREFS
Column k=8 of A271423.
Sequence in context: A305069 A061658 A254147 * A280887 A158630 A158634
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 13 2016
STATUS
approved