A343790 Number of ordered partitions of an n-set without blocks of size 7.

1, 1, 3, 13, 75, 541, 4683, 47292, 545819, 7086973, 102242283, 1622530933, 28089498891, 526813752973, 10640325166227, 230258631645913, 5315029292965675, 130353994525735677, 3385061859378821547, 92787606222541942477, 2677254928352340708075, 81110818086045534369661

Offset

0,3

Links

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

Formula

E.g.f.: 1 / (2 + x^7/7! - exp(x)).

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      `if`(j=7, 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^7/7! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 7, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]

Crossrefs

Cf. A000670, A032032, A337058, A337059, A343667, A343787, A343788, A343789, A343791, A343792, A343793.

Sequence in context: A343789 A276896 A276926 * A276897 A276927 A343791

Adjacent sequences: A343787 A343788 A343789 * A343791 A343792 A343793

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 29 2021

Status

approved