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A161799
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G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^2)^3.
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3
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1, 3, 12, 61, 345, 2085, 13182, 86106, 576543, 3936029, 27294390, 191722887, 1361291244, 9754412169, 70447946556, 512278417176, 3747570671685, 27561220671408, 203657352324178, 1511270129552163, 11257532921742528
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} C(3*n-2*k+2,k)/(n-k+1) * C(n+k-1,n-k).
Let A(x)^m = Sum_{n>=0} a(n,m)*x^n then
a(n,m) = Sum_{k=0..n} C(3*n-2*k+3*m-1,k)*m/(n-k+m) * C(n+k-1,n-k).
a(n) ~ c*d^n/(sqrt(Pi)*n^(3/2)), where d = 8.01957328653868383... is the root of the equation 3125 + 22356*d - 162432*d^2 - 361584*d^3 - 326592*d^4 + 46656*d^5 = 0 and c = 1.56703431595354192843152170651865561188... - Vaclav Kotesovec, Sep 18 2013
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MAPLE
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local s, t ;
s := 2 ;
t := 3;
add( binomial(t*n-(t-1)*(k-1), k) * binomial(n+(s-1)*k-1, n-k) /(n-k+1) , k=0..n) ;
end proc:
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MATHEMATICA
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Table[Sum[Binomial[3*n-2*k+2, k]/(n-k+1)*Binomial[n+k-1, n-k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 18 2013 *)
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PROG
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(PARI) {a(n, m=1)=sum(k=0, n, binomial(3*n-2*k+3*m-1, k)*m/(n-k+m)*binomial(n+k-1, n-k))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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