0,3

G.f. satisfies: A(x) = F(x/A(x)^2) and F(x) = A(x*F(x)^2) where F(x) = Sum_{n>=0} A155926(n)*x^n/[n!*(n+1)!/2^n].

G.f. satisfies: A(x) = 1/G(x/A(x)) and G(x) = 1/A(x/G(x)) where G(x) = Sum_{n>=0} A103365(n)*x^n/[n!*(n+1)!/2^n].

G.f.: A(x) = 1 + x - 2*x^2/3 + 19*x^3/18 - 379*x^4/180 + 12726*x^5/2700 +...+ a(n)*x^n/[n!*(n+1)!/2^n] +...

G.f. satisfies: A(x) = B(x/A(x)) and B(x) = A(x*B(x)) where:

B(x) = 1 + x + 1/3*x^2 + 1/18*x^3 + 1/180*x^4 +...+ x^n/[n!*(n+1)!/2^n] +...

G.f. satisfies: A(x) = F(x/A(x)^2) and F(x) = 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+1)/[n!*(n+1)!/2^n] +...

G.f. satisfies: A(x) = 1/G(x/A(x)) and G(x) = 1/A(x/G(x)) where:

G(x) = 1 - x + 2*x^2/3 - 7*x^3/18 + 39*x^4/180 - 321*x^5/2700 +...+ A103365(n)*x^(n+1)/[n!*(n+1)!/2^n] +...

(PARI) {a(n)=local(B=sum(k=0, n, x^k/(k!*(k+1)!/2^k))+x*O(x^n)); polcoeff(x/serreverse(x*B), n)*n!*(n+1)!/2^n}

Cf. A155926, A103365.

Sequence in context: A078369 A090308 A110818 this_sequence A120420 A158099 A015204

Adjacent sequences: A155924 A155925 A155926 this_sequence A155928 A155929 A155930

sign

Paul D. Hanna (pauldhanna(AT)juno.com), Jan 31 2009