A343791 Number of ordered partitions of an n-set without blocks of size 8.

1, 1, 3, 13, 75, 541, 4683, 47293, 545834, 7087243, 102247203, 1622625313, 28091415135, 526854986737, 10641264928479, 230281282588513, 5315605563021465, 130369438065006551, 3385496924633886429, 92800464391224494215, 2677652842774247060805, 81123688691904430522831

Offset: 0

Author

Ilya Gutkovskiy, Apr 29 2021

Keywords

• nonn

Crossrefs

Cf. A000670, A032032, A337058, A337059, A343668, A343787, A343788, A343789, A343790, A343792, A343793.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      `if`(j=8, 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^8/8! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 8, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]

Formula

E.g.f.: 1 / (2 + x^8/8! - exp(x)).