A193932 E.g.f. A(x) = exp(x+x^2+x^3+x^4+x^5+x^6).

1, 1, 3, 13, 73, 501, 4051, 32593, 313713, 3326473, 38377891, 476464341, 6299024953, 87715975933, 1314012177843, 20776583119321, 345267365639521, 6009277853650833, 109262845394221123, 2073062512187103133, 41084832105634595241, 845645768972241105541

Offset: 0

Author

Vladimir Kruchinin, Aug 09 2011

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..485

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-j)*binomial(n-1, j-1)*j!, j=1..min(n, 6)))
    end:
seq(a(n), n=0..23);  # Alois P. Heinz, Sep 29 2017

Mathematica

With[{nn=20},CoefficientList[Series[Exp[Total[x^Range[6]]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Oct 12 2015 *)

Maxima

a(n):=if n=0 then 1 else n!*sum(sum((-1)^i*binomial(k, k-i)*binomial(n-6*i-1, k-1), i, 0, (n-k)/6)/k!, k, 1, n);

Formula

a(n)=n!*sum(k=1..n, sum(i=0..(n-k)/6, (-1)^i*binomial(k,k-i)*binomial(n-6*i-1,k-1))/k!), n>0, a(0)=1.