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A025229
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a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 3.
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7
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1, 3, 6, 21, 78, 318, 1356, 5997, 27222, 126138, 594132, 2836290, 13692300, 66729180, 327855768, 1622216829, 8076311142, 40427919714, 203353800324, 1027318915254, 5210182030308, 26517609163812, 135397544040744, 693364054299474
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} 2^(n-k)*C(k)*C(k+1, n-k) [offset 0]. - Paul Barry, Feb 22 2005
Another recurrence formula: n*a(n) = (4*n-6)*a(n-1)+(8*n-24)*a(n-2). - Richard Choulet, Dec 16 2009
a(n) ~ sqrt(3-sqrt(3))*(2+2*sqrt(3))^n/(4*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 07 2012
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MAPLE
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option remember;
if n <=1 then
n;
elif n = 2 then
3;
else
add( procname(n-i)*procname(i), i=1..n-1) ;
end if;
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MATHEMATICA
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Table[SeriesCoefficient[(1-Sqrt[1-4*x-8*x^2])/2, {x, 0, n}], {n, 1, 20}] (* Vaclav Kotesovec, Oct 07 2012 *)
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PROG
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(PARI) a(n)=polcoeff((1-sqrt(1-4*x-8*x^2+x*O(x^n)))/2, n)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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