|
|
A343793
|
|
Number of ordered partitions of an n-set without blocks of size 10.
|
|
6
|
|
|
1, 1, 3, 13, 75, 541, 4683, 47293, 545835, 7087261, 102247562, 1622632551, 28091567067, 526858335797, 10641342662135, 230283183134017, 5315654473869451, 130370761261559229, 3385534496252337939, 92801582269262225397, 2677687636903407184463, 81124819758167172293305
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: 1 / (2 + x^10/10! - exp(x)).
|
|
MAPLE
|
a:= proc(n) option remember; `if`(n=0, 1, add(
`if`(j=10, 0, a(n-j)*binomial(n, j)), j=1..n))
end:
|
|
MATHEMATICA
|
nmax = 21; CoefficientList[Series[1/(2 + x^10/10! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 10, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]
|
|
CROSSREFS
|
Cf. A000670, A032032, A337058, A337059, A343671, A343787, A343788, A343789, A343790, A343791, A343792.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|