A193100 E.g.f. A(x) satisfies: A’(x) = x + A(A(x)), where A(x) = Sum_{n>=0} a(n)*x^(3*n+2)/(3*n+2)!.

1, 3, 63, 6804, 1990170, 1145276496, 1172421884088, 1981846981092069, 5166650461467914874, 19710026486212156729362, 105613632141369240315500892, 768455476842781911036557334267, 7380326961188107570497477933701847

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Example

E.g.f.: A(x) = x^2/2! + 3*x^5/5! + 63*x^8/8! + 6804*x^11/11! + 1990170*x^14/14! + 1145276496*x^17/17! + 1172421884088*x^20/20! +...
where A'(x) = x + 3*x^4/4! + 63*x^7/7! + 6804*x^10/10! +...
and A(A(x)) = 3*x^4/4! + 63*x^7/7! + 6804*x^10/10! + 1990170*x^13/13! +...

Prog

(PARI) {a(n)=local(A=x^2/2); for(i=1, n, A=intformal(x+subst(A, x, A+O(x^(3*n+3))))); (3*n+2)!*polcoeff(A, 3*n+2)}

Crossrefs

Cf. A001028, A179420.

Sequence in context: A159605 A180761 A156904 * A053857 A175985 A037108

Adjacent sequences: A193097 A193098 A193099 * A193101 A193102 A193103

Keyword

nonn

Author

Paul D. Hanna, Jul 15 2011

Status

approved