OFFSET
0,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
K. Anders and K. Archer, Rooted forests that avoid sets of permutations, arXiv:1607.03046 [math.CO], 2017.
FORMULA
a(n) = Sum_{k=1..n} Sum_{r=1..k} binomial(n-1,k-1)*(r-1)!*a(n-k)*a(k-r) for n>0, a(0)=1.
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n-1, k-1] (r-1)! a[n-k] a[k-r], {k, 1, n}, {r, 1, k}];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Sep 13 2018 *)
PROG
(PARI) seq(n)={my(v=vector(n+1)); v[1]=1; for(n=1, n, v[n+1]=sum(k=1, n, sum(r=1, k, binomial(n-1, k-1)*(r-1)!*v[n-k+1]*v[k-r+1]))); v} \\ Andrew Howroyd, Aug 30 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Kassie Archer, Aug 30 2018
STATUS
approved