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A032036
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Shifts left 3 places under "AIJ" (ordered, indistinct, labeled) transform.
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1
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1, 1, 1, 1, 3, 13, 75, 543, 4719, 47871, 555177, 7245015, 105069249, 1676322369, 29178875913, 550266979833, 11176051287627, 243213176948013, 5645877335588331, 139257558038636847, 3636985088689068231, 100266394939348499127, 2909740575643004791953, 88664517647380019280375
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OFFSET
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1,5
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LINKS
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FORMULA
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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
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,eigen
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AUTHOR
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STATUS
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approved
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