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

0,3

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!.

Links

Table of n, a(n) for n=0..18.

Example

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! +...

Prog

(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), ", "))

Crossrefs

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

Sequence in context: A196958 A274246 A161567 * A141006 A372168 A367835

Adjacent sequences: A213106 A213107 A213108 * A213110 A213111 A213112

Keyword

nonn

Author

Paul D. Hanna, Jun 05 2012

Status

approved