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A271762 Number of set partitions of [n] with minimal block length multiplicity equal to two. 2
1, 0, 3, 0, 55, 105, 945, 1218, 15456, 26785, 705573, 2502786, 32988670, 169561483, 1757881723, 10231748010, 84389906941, 540218433147, 6899156019034, 41756989590256, 554960234199955, 4793361957432730, 59690079139252499, 558283841454550850, 7093218105977514525 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,3
LINKS
FORMULA
a(n) = A271424(n,2).
EXAMPLE
a(4) = 3: 12|34, 13|24, 14|23.
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, 2)-b(n$2, 3):
seq(a(n), n=2..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, 2] - b[n, n, 3];
Table[a[n], {n, 2, 30}] (* Jean-François Alcover, May 15 2018, after Alois P. Heinz *)
CROSSREFS
Column k=2 of A271424.
Sequence in context: A009786 A012738 A193410 * A264882 A012759 A296621
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 13 2016
STATUS
approved

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Last modified July 20 18:59 EDT 2024. Contains 374459 sequences. (Running on oeis4.)