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A032036 Shifts left 3 places under "AIJ" (ordered, indistinct, labeled) transform. 1

%I #18 Sep 20 2018 02:57:58

%S 1,1,1,1,3,13,75,543,4719,47871,555177,7245015,105069249,1676322369,

%T 29178875913,550266979833,11176051287627,243213176948013,

%U 5645877335588331,139257558038636847,3636985088689068231,100266394939348499127,2909740575643004791953,88664517647380019280375

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

%H Andrew Howroyd, <a href="/A032036/b032036.txt">Table of n, a(n) for n = 1..200</a>

%F 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

%F 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

%o (Maxima)

%o 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 */

%o (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

%K nonn,eigen

%O 1,5

%A _Christian G. Bower_

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)