A213112 E.g.f.: A(x) = exp( x/A(-x*A(x)^7)^3 ).

1, 1, 7, 118, 2953, 109156, 5220649, 316358470, 23113133089, 1989812691208, 196917302640241, 22027382030604226, 2745173167377165793, 376884883299800082988, 56471832695739964146505, 9164249250078891945300886, 1600258838038369930772797249

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 + 7*x^2/2! + 118*x^3/3! + 2953*x^4/4! + 109156*x^5/5! +...
Related expansions:
A(x)^3 = 1 + 3*x + 27*x^2/2! + 486*x^3/3! + 12825*x^4/4! + 477108*x^5/5! +...
A(x)^7 = 1 + 7*x + 91*x^2/2! + 1918*x^3/3! + 56329*x^4/4! + 2194612*x^5/5! +...
1/A(-x*A(x)^7)^3 = 1 + 3*x + 33*x^2/2! + 603*x^3/3! + 17913*x^4/4! +...
The logarithm of the e.g.f., log(A(x)) = x/A(-x*A(x)^7)^3, begins:
log(A(x)) = x + 6*x^2/2! + 99*x^3/3! + 2412*x^4/4! + 89565*x^5/5! +...
		

Crossrefs

Cf. A213108, A213109, A213110, A213111, A213113.

Programs

PARI

{a(n)=local(A=1+x);for(i=1,n,A=exp(x/subst(A^3,x,-x*A^7+x*O(x^n))));n!*polcoeff(A,n)}
for(n=0,25,print1(a(n),", "))