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A271763 Number of set partitions of [n] with minimal block length multiplicity equal to three. 2
1, 0, 0, 15, 0, 0, 1540, 3150, 24255, 81235, 496210, 605605, 36987951, 13833820, 849333940, 24419945732, 111237098546, 1219799147204, 16146398449224, 109697049177254, 1037441240056529, 9042707959752775, 84237798887033660, 614681985047225810 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,4
LINKS
FORMULA
a(n) = A271424(n,3).
EXAMPLE
a(6) = 15: 12|34|56, 12|35|46, 12|36|45, 13|24|56, 13|25|46, 13|26|45, 14|23|56, 15|23|46, 16|23|45, 14|25|36, 14|26|35, 15|24|36, 16|24|35, 15|26|34, 16|25|34.
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, $k..n/i})))
end:
a:= n-> b(n$2, 3)-b(n$2, 4):
seq(a(n), n=3..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, Join[{0}, Range[k, n/i]]}]]];
a[n_] := b[n, n, 3] - b[n, n, 4];
Table[a[n], {n, 3, 30}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *)
CROSSREFS
Column k=3 of A271424.
Sequence in context: A324677 A324675 A106239 * A362267 A271339 A202857
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 13 2016
STATUS
approved

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Last modified July 19 02:27 EDT 2024. Contains 374388 sequences. (Running on oeis4.)