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

0,3

Links

Table of n, a(n) for n=0..21.

Formula

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

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}]

Crossrefs

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

Sequence in context: A343790 A276897 A276927 * A276898 A276928 A343792

Adjacent sequences: A343788 A343789 A343790 * A343792 A343793 A343794

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 29 2021

Status

approved