A343789 Number of ordered partitions of an n-set without blocks of size 6.

1, 1, 3, 13, 75, 541, 4682, 47279, 545611, 7083565, 102182883, 1621425829, 28067555607, 526349480593, 10629883138059, 230009622202373, 5308749619032571, 130186940173803053, 3380385112758108315, 92650130825921846941, 2673020491585091254035, 80974418589343644492805

Offset

0,3

Links

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

Formula

E.g.f.: 1 / (2 + x^6/6! - exp(x)).

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      `if`(j=6, 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^6/6! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 6, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]

Crossrefs

Cf. A000670, A032032, A337058, A337059, A343666, A343787, A343788, A343790, A343791, A343792, A343793.

Sequence in context: A343788 A276895 A276925 * A276896 A276926 A343790

Adjacent sequences: A343786 A343787 A343788 * A343790 A343791 A343792

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 29 2021

Status

approved