A213108 E.g.f.: A(x) = exp( x/A(-x*A(x)) ).

1, 1, 3, 10, 41, 76, -2183, -54998, -1045567, -15948296, -157645999, 2035442014, 217585291057, 10000385378452, 373813151971001, 11759936127330346, 269243105500780673, -519586631788126352, -649842878319124373855, -59793494397006229506890

Offset: 0

Author

Paul D. Hanna, Jun 05 2012

Keywords

• sign

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! + 10*x^3/3! + 41*x^4/4! + 76*x^5/5! - 2183*x^6/6! +...
Related expansions:
1/A(-x*A(x)) = 1 + x + x^2/2! + x^3/3! - 23*x^4/4! - 419*x^5/5! - 5159*x^6/6! +...
The logarithm of the e.g.f., log(A(x)) = x/A(-x*A(x)), begins:
log(A(x)) = x + 2*x^2/2! + 3*x^3/3! + 4*x^4/4! - 115*x^5/5! - 2514*x^6/6! - 36113*x^7/7! +...
		

Crossrefs

Cf. A213109, A213110, A213111, A213112, A213113.

Programs

PARI

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