A343788 Number of ordered partitions of an n-set without blocks of size 5.

1, 1, 3, 13, 75, 540, 4671, 47125, 543371, 7048453, 101589591, 1610634433, 27856938387, 521953586233, 10532102378983, 227699187663961, 5250934660206219, 128659152359921997, 3337861722359261475, 91406502629924948053, 2634888477782107003707, 79751100251346500871481

Offset: 0

Author

Ilya Gutkovskiy, Apr 29 2021

Keywords

• nonn

Crossrefs

Cf. A000670, A032032, A337058, A337059, A343665, A343787, A343789, A343790, A343791, A343792, A343793.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      `if`(j=5, 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^5/5! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 5, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]

Formula

E.g.f.: 1 / (2 + x^5/5! - exp(x)).