OFFSET
0,2
FORMULA
G.f. satisfies: A(x) = B( x*sqrt(A(x)) )^2 where B(x) = Sum_{n>=0} x^n/[n!*(n+1)!/2^n].
EXAMPLE
G.f.: A(x) = 1 + 2*x + 11*x^2/3 + 122*x^3/18 + 2302*x^4/180 + 66482*x^5/2700 +...
G.f.: A(x) = F(x)^2 where:
F(x) = 1 + x + 4*x^2/3 + 37*x^3/18 + 621*x^4/180 + 16526*x^5/2700 +...+ A155926(n)*x^n/[n!*(n+1)!/2^n] +...
G.f. satisfies: A(x) = B( x*sqrt(A(x)) )^2 where:
B(x) = 1 + x + x^2/3 + x^3/18 + x^4/180 + x^5/2700 +...+ x^n/[n!*(n+1)!/2^n] +...
PROG
(PARI) {a(n)=local(B=sum(k=0, n, x^k/(k!*(k+1)!/2^k))+x*O(x^n)); polcoeff((serreverse(x/B)/x)^2, n)*n!*(n+1)!/2^n}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 31 2009
STATUS
approved