A193931 E.g.f. A(x) = exp(x+x^2+x^3+x^4+x^5).

1, 1, 3, 13, 73, 501, 3331, 27553, 253233, 2540233, 27340291, 309811701, 3843476473, 50560182973, 701098196163, 10205952248521, 155809733115361, 2506135027165713, 42013633806350083, 732584456250306013, 13270900741926553641, 249625454707702681861

Offset: 0

Author

Vladimir Kruchinin, Aug 09 2011

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

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, 5)))
    end:
seq(a(n), n=0..23);  # Alois P. Heinz, Sep 29 2017

Maxima

a(n):=if n=0 then 1 else n!*sum(sum((-1)^i*binomial(k,k-i)*binomial(n-5*i-1,k-1),i,0,(n-k)/5)/k!,k,1,n);

Formula

a(n)=n!*sum(k=1..n, sum(i=0..(n-k)/5, (-1)^i*binomial(k,k-i)*binomial(n-5*i-1,k-1))/k!), n>0, a(0)=1.

E.g.f.: 1 + x*(E(0)-1)/(x+1) where E(k) = 1 + (1+x+x^2+x^3+x^4)/(k+1)/(1-x/(x+1/E(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 27 2013