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A287671
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-8 is member of a block >= b-1.
2
1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678569, 4213333, 27634757, 190697165, 1379679500, 10433619205, 82253035850, 674373619108, 5738060816421, 50573749394877, 460936356129618, 4337525923676113, 42084057817903853, 420444371318055912
OFFSET
0,3
LINKS
FORMULA
a(n) = A287641(n,8).
a(n) = A000110(n) for n <= 10.
EXAMPLE
a(11) = 678569 = 678570 - 1 = A000110(11) - 1 counts all set partitions of [11] except: 13456789(10)|2|(11).
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$8]):
seq(a(n), n=0..20);
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, 8]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 27 2018, from Maple *)
CROSSREFS
Column k=8 of A287641.
Cf. A000110.
Sequence in context: A287588 A287281 A287259 * A164864 A366776 A192866
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 29 2017
STATUS
approved