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%I #6 May 21 2018 02:33:55
%S 1,1,2,8,52,504,6808,122304,2820048,81183200,2853990496,120321094656,
%T 5991955466560,347996920977664,23312947041336960,1784445116557881344,
%U 154767015393810489600,15098457734490931766784
%N a(n) = Sum_{k=0..n} C(n-1,k)^2*a(k)*a(n-k-1) for n>0 with a(0)=1.
%C Let A(x) = Sum_{n>=0} a(n) * x^n / n!^2. Then A(x)^2 = A'(x) + x * A''(x). - _Michael Somos_, May 20 2018
%o (PARI) a(n)=if(n==0,1,sum(k=0,n-1,a(k)*a(n-k-1)*binomial(n-1,k)^2 ))
%o (PARI) {a(n) = my(A); if( n<0, 0, A = 1 + O(x); for( k=0, n, A = 1 + intformal( intformal(A^2) / x)); n!^2 * polcoeff(A,n))}; /* _Michael Somos_, May 20 2018 */
%Y Cf. A001059.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 15 2007
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