A213110 E.g.f.: A(x) = exp( x/A(-x*A(x)^5)^2 ).

1, 1, 5, 61, 1089, 29081, 1006753, 44229669, 2338846849, 145278355825, 10340497436481, 829144792315709, 73858518558797569, 7228342584930637353, 770235745321038739681, 88690109534418912004501, 10965585032265975064491777, 1447844650991790389918127329

Offset: 0

Author

Paul D. Hanna, Jun 05 2012

Keywords

• nonn

Comments

Compare the e.g.f. to:

(1) W(x) = exp(x/W(-x*W(x)^2)^1) when W(x) = Sum_{n>=0} (1*n+1)^(n-1)*x^n/n!.

(2) W(x) = exp(x/W(-x*W(x)^4)^2) when W(x) = Sum_{n>=0} (2*n+1)^(n-1)*x^n/n!.

(3) W(x) = exp(x/W(-x*W(x)^6)^3) when W(x) = Sum_{n>=0} (3*n+1)^(n-1)*x^n/n!.

Examples

			E.g.f.: A(x) = 1 + x + 5*x^2/2! + 61*x^3/3! + 1089*x^4/4! + 29081*x^5/5! +...
Related expansions:
A(x)^2 = 1 + 2*x + 12*x^2/2! + 152*x^3/3! + 2816*x^4/4! + 75152*x^5/5! +...
A(x)^5 = 1 + 5*x + 45*x^2/2! + 665*x^3/3! + 13745*x^4/4! + 380525*x^5/5! +...
1/A(-x*A(x)^5)^2 = 1 + 2*x + 16*x^2/2! + 206*x^3/3! + 4456*x^4/4! +...
The logarithm of the e.g.f., log(A(x)) = x/A(-x*A(x)^5)^2, begins:
log(A(x)) = x + 4*x^2/2! + 48*x^3/3! + 824*x^4/4! + 22280*x^5/5! + 774012*x^6/6! +...
		

Crossrefs

Cf. A213108, A213109, A213111, A213112, A213113.

Programs

PARI

{a(n)=local(A=1+x);for(i=1,n,A=exp(x/subst(A^2,x,-x*A^5+x*O(x^n))));n!*polcoeff(A,n)}
for(n=0,25,print1(a(n),", "))