A155927 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].

1, 1, -2, 19, -379, 12726, -641465, 45181627, -4232016719, 508271819428, -76108505872794, 13896010073569130, -3038043685025188631, 783439451518414509612, -235289860249420249309140

Offset: 0

Author

Paul D. Hanna, Jan 31 2009

Keywords

• sign

Examples

			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] +...
		

Crossrefs

Cf. A155926, A103365.

Programs

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}

Formula

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].