A132228 a(n) = Sum_{k=0..n} C(n-1,k)^2*a(k)*a(n-k-1) for n>0 with a(0)=1.

1, 1, 2, 8, 52, 504, 6808, 122304, 2820048, 81183200, 2853990496, 120321094656, 5991955466560, 347996920977664, 23312947041336960, 1784445116557881344, 154767015393810489600, 15098457734490931766784

Offset: 0

Author

Paul D. Hanna, Aug 15 2007

Keywords

• nonn

Comments

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

Crossrefs

Cf. A001059.

Programs

PARI

a(n)=if(n==0,1,sum(k=0,n-1,a(k)*a(n-k-1)*binomial(n-1,k)^2 ))

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 */