A213113 E.g.f.: A(x) = exp( x/A(-x*A(x)^9)^3 ).

1, 1, 7, 154, 4681, 228076, 14299129, 1138327282, 108153498625, 11945906543512, 1500579818594641, 210620216812835446, 32619162944121580369, 5512919937646519781956, 1007971183370936380058233, 197907153405452704613136466, 41467801090663272520003650049

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!.

(4) W(x) = exp(x/W(-x*W(x)^8)^4) when W(x) = Sum_{n>=0} (4*n+1)^(n-1)*x^n/n!.

Examples

			E.g.f.: A(x) = 1 + x + 7*x^2/2! + 154*x^3/3! + 4681*x^4/4! + 228076*x^5/5! +...
Related expansions:
A(x)^3 = 1 + 3*x + 27*x^2/2! + 594*x^3/3! + 18873*x^4/4! + 902988*x^5/5! +...
A(x)^9 = 1 + 9*x + 135*x^2/2! + 3402*x^3/3! + 121257*x^4/4! + 5887404*x^5/5! +...
1/A(-x*A(x)^9)^3 = 1 + 3*x + 45*x^2/2! + 999*x^3/3! + 39609*x^4/4! +...
The logarithm of the e.g.f., log(A(x)) = x/A(-x*A(x)^9)^3, begins:
log(A(x)) = x + 6*x^2/2! + 135*x^3/3! + 3996*x^4/4! + 198045*x^5/5! +...
		

Crossrefs

Cf. A213108, A213109, A213110, A213111, A213112.

Programs

PARI

{a(n)=local(A=1+x);for(i=1,n,A=exp(x/subst(A^3,x,-x*A^9+x*O(x^n))));n!*polcoeff(A,n)}
for(n=0,25,print1(a(n),", "))