OFFSET
1,5
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
FORMULA
a(n) = sum(k=0..n-4, binomial(n-3,k)*a(k+3)*a(n-k-3)), a(1)=a(2)=a(3)=1. - Vladimir Kruchinin, May 10 2011
E.g.f. A(x) satisfies differential equation A'''(x)-A(x)*A'''(x)=1, A'(0)=1, A''(0)=1, A'''(0)=1. - Vladimir Kruchinin, Nov 19 2011
PROG
(Maxima)
a(n):=if n=0 then 0 else if n<4 then 1 else sum(binomial(n-3, k)*a(k+3)*a(n-k-3), k, 0, n-4); /* Vladimir Kruchinin, May 10 2011 */
(PARI) seq(n)={my(p=x+x^2+O(x*x^(n%3))); for(i=1, n\3, p=intformal(1 + intformal(1 + intformal(1/(1-p))))); Vec(serlaplace(p))} \\ Andrew Howroyd, Sep 19 2018
CROSSREFS
KEYWORD
nonn,eigen
AUTHOR
STATUS
approved