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FORMULA
a(n) ~ c * (n!)^2 / (2^n * n^(1/3)), where c = 3.081214203431821156695905553610151693827575050546... - Vaclav Kotesovec, Feb 20 2014
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MATHEMATICA
a = ConstantArray[0, 20]; a[[1]]=1; Do[a[[n]] = Sum[Binomial[n, k-1]*a[[n-k]]*a[[k]], {k, 1, n-1}], {n, 2, 20}]; a (* Vaclav Kotesovec, Feb 19 2014 *)
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LINKS
Vaclav Kotesovec, <a href="/A229548/b229548.txt">Table of n, a(n) for n = 1..200</a>
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NAME
E.g.f. satisfies: A(x) = x + A'(x) * Integral A(x) dx.
FORMULA
a(n) = Sum_{k=1..n-1} binomial(n,k-1)*a(n-k)*a(k) for n>1 with a(1)=1.
EXAMPLE
E.g.f.: A(x) = x + x^2/2! + 4*x^3/3! + 32*x^4/4! + 412*x^5/5! + 7664*x^6/6! +...
so that B(x) = Integral A(x) dx (here integration does not include constant term).
PROG
(PARI) {a(n)=local(A=x+x^2); for(i=1, n, A=x+A'*intformal(A+x*O(x^n))); n!*polcoeff(A, n)}
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