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

0,3

Links

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

Formula

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

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}]

Crossrefs

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

Sequence in context: A349533 A020094 A189886 * A333890 A009382 A110193

Adjacent sequences: A343784 A343785 A343786 * A343788 A343789 A343790

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 29 2021

Status

approved