A343792 Number of ordered partitions of an n-set without blocks of size 9.

1, 1, 3, 13, 75, 541, 4683, 47293, 545835, 7087260, 102247543, 1622632133, 28091557915, 526858128161, 10641337741219, 230283060907913, 5315651289289195, 130370674248854021, 3385532005327322503, 92801507648842580769, 2677685300845992661475, 81124743440296074264381

Offset: 0

Author

Ilya Gutkovskiy, Apr 29 2021

Keywords

• nonn

Crossrefs

Cf. A000670, A032032, A337058, A337059, A343669, A343787, A343788, A343789, A343790, A343791, A343793.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      `if`(j=9, 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^9/9! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 9, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]

Formula

E.g.f.: 1 / (2 + x^9/9! - exp(x)).