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A287668
Number of set partitions of [n] such that j is member of block b only if b = 1 or at least one of j-1, ..., j-5 is member of a block >= b-1.
2
1, 1, 2, 5, 15, 52, 203, 877, 4139, 21107, 115301, 670059, 4119316, 26665103, 181031235, 1284643851, 9500643629, 73037739470, 582346938182, 4805997066022, 40980051074202, 360452146946076, 3265691382361850, 30435437254066599, 291431082211368120
OFFSET
0,3
LINKS
FORMULA
a(n) = A287641(n,5).
a(n) = A000110(n) for n <= 7.
EXAMPLE
a(8) = 4139 = 4140 - 1 = A000110(8) - 1 counts all set partitions of [8] except: 134567|2|8.
MAPLE
b:= proc(n, l) option remember; `if`(n=0, 1, add(b(n-1,
[seq(max(l[i], j), i=2..nops(l)), j]), j=1..l[1]+1))
end:
a:= n-> b(n, [0$5]):
seq(a(n), n=0..24);
MATHEMATICA
b[n_, l_] := b[n, l] = If[n == 0, 1, Sum[b[n - 1, Append[Table[Max[l[[i]], j], {i, 2, Length[l]}], j]], {j, 1, l[[1]] + 1}]];
a[n_] := b[n, Table[0, {5}]];
a /@ Range[0, 24] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)
CROSSREFS
Column k=5 of A287641.
Cf. A000110.
Sequence in context: A287585 A287278 A287256 * A099262 A141081 A108305
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 29 2017
STATUS
approved