A155927 - OEIS

%I #2 Mar 30 2012 18:37:16

%S 1,1,-2,19,-379,12726,-641465,45181627,-4232016719,508271819428,

%T -76108505872794,13896010073569130,-3038043685025188631,

%U 783439451518414509612,-235289860249420249309140

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

%F 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].

%F 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].

%e 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] +...

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

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

%e G.f. satisfies: A(x) = F(x/A(x)^2) and F(x) = A(x*F(x)^2) where:

%e 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] +...

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

%e 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] +...

%o (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}

%Y Cf. A155926, A103365.

%K sign

%O 0,3

%A _Paul D. Hanna_, Jan 31 2009