A032036 Shifts left 3 places under "AIJ" (ordered, indistinct, labeled) transform.

1, 1, 1, 1, 3, 13, 75, 543, 4719, 47871, 555177, 7245015, 105069249, 1676322369, 29178875913, 550266979833, 11176051287627, 243213176948013, 5645877335588331, 139257558038636847, 3636985088689068231, 100266394939348499127, 2909740575643004791953, 88664517647380019280375

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

Sequence in context: A276930 A034172 A000670 * A305535 A300793 A222427

Adjacent sequences: A032033 A032034 A032035 * A032037 A032038 A032039

Keyword

nonn,eigen

Author

Christian G. Bower

Status

approved