|
|
A287673
|
|
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-10 is member of a block >= b-1.
|
|
2
|
|
|
1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644436, 190898290, 1382887161, 10477990158, 82819430415, 681282289857, 5820296183791, 51541816775857, 472306124149579, 4471549108520595, 43676154621078016, 439558508006341652
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
a(13) = 27644436 = 27644437 - 1 = A000110(13) - 1 counts all set partitions of [13] except: 13456789(10)(11)(12)|2|(13).
|
|
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$10]):
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, 10]];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|