A343787 Number of ordered partitions of an n-set without blocks of size 4.

1, 1, 3, 13, 74, 531, 4563, 45753, 524345, 6760039, 96837333, 1525909903, 26230304235, 488472319271, 9796281435125, 210496933103743, 4824574494068495, 117490079786298641, 3029472152485535343, 82454398253005541089, 2362311059301928969755, 71063998308414194250901

Offset: 0

Author

Ilya Gutkovskiy, Apr 29 2021

Keywords

• nonn

Crossrefs

Cf. A000670, A032032, A337058, A337059, A343664, A343788, A343789, A343790, A343791, A343792, A343793.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      `if`(j=4, 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^4/4! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 4, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]

Formula

E.g.f.: 1 / (2 + x^4/4! - exp(x)).