A343793 Number of ordered partitions of an n-set without blocks of size 10.
1, 1, 3, 13, 75, 541, 4683, 47293, 545835, 7087261, 102247562, 1622632551, 28091567067, 526858335797, 10641342662135, 230283183134017, 5315654473869451, 130370761261559229, 3385534496252337939, 92801582269262225397, 2677687636903407184463, 81124819758167172293305
Offset: 0
Keywords
Crossrefs
Programs
-
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: seq(a(n), n=0..21); # Alois P. Heinz, Apr 29 2021 -
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}]
Formula
E.g.f.: 1 / (2 + x^10/10! - exp(x)).