A213109 E.g.f.: A(x) = exp( x/A(-x*A(x)^3) ).

1, 1, 3, 22, 233, 3716, 77257, 2026606, 63726497, 2333516392, 97335801521, 4543398147674, 234240366949921, 13191513757571644, 804299893048589225, 52696560194440470046, 3686739789058021079873, 273950438842854064788560, 21522076959435116533294177

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 + 3*x^2/2! + 22*x^3/3! + 233*x^4/4! + 3716*x^5/5! +...
Related expansions:
A(x)^3 = 1 + 3*x + 15*x^2/2! + 126*x^3/3! + 1497*x^4/4! + 24228*x^5/5! +...
1/A(-x*A(x)^3) = 1 + x + 5*x^2/2! + 37*x^3/3! + 489*x^4/4! + 8541*x^5/5! +...
The logarithm of the e.g.f., log(A(x)) = x/A(-x*A(x)^3), begins:
log(A(x)) = x + 2*x^2/2! + 15*x^3/3! + 148*x^4/4! + 2445*x^5/5! + 51246*x^6/6! +...
		

Crossrefs

Cf. A213108, A213110, A213111, A213112, A213113.

Programs

PARI

{a(n)=local(A=1+x);for(i=1,n,A=exp(x/subst(A,x,-x*A^3+x*O(x^n))));n!*polcoeff(A,n)}
for(n=0,25,print1(a(n),", "))