A293025 E.g.f.: exp(exp(x) - Sum_{i=0..5} x^i/i!).

1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 463, 1717, 4720, 11441, 25884, 56135, 2977313, 23524737, 125212889, 552517341, 2183244857, 8025931950, 124257251233, 1468856487536, 12433365625566, 85767520652726, 518324768774506, 2858925345803536, 26181976719735061

Offset: 0

Author

Seiichi Manyama, Sep 28 2017

Keywords

• nonn

Comments

a(n) is the number of set partitions of [n] into blocks of size > 5.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..595

Crossrefs

Column k=5 of A293024.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-j)*binomial(n-1, j-1), j=6..n))
    end:
seq(a(n), n=0..35);  # Alois P. Heinz, Sep 28 2017

Mathematica

m = 31;
Exp[Exp[x] - Sum[x^i/i!, {i, 0, 5}]] + O[x]^m // CoefficientList[#, x]& // (# Range[0, m-1]!)& (* Jean-François Alcover, Mar 08 2021 *)

PARI

my(x='x+O('x^66)); Vec(serlaplace(exp(exp(x)-1-x-x^2/2-x^3/6-x^4/24-x^5/120)))

Formula

E.g.f.: Product_{i>5} exp(x^i/i!).