A193265 E.g.f. A(x) = G(x)/x where G(x) satisfies: G(G(G(x))) = 2*x*G'(x) - G(x).

1, 1, 6, 81, 1828, 59910, 2629800, 146775160, 10047085200, 821599116300, 78674552192800, 8684916065005620, 1091429676788178240, 154543476785542516360, 24445478524707259098240, 4288239906998845117572000, 829048705765475214447735040

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..149

Formula

a(n) = A193264(n+1)/(n+1).

Example

E.g.f.: A(x) = 1 + x + 6*x^2/2! + 81*x^3/3! + 1828*x^4/4! + 59910*x^5/5! +...
Let G(x) = x*A(x), then:
G(G(G(x))) = x + 6*x^2/2! + 90*x^3/3! + 2268*x^4/4! + 82260*x^5/5! +...+ (2*n-1)*n*a(n-1)*x^n/n! +...
which equals 2*x*G'(x) - G(x) = x*A(x) + 2*x^2*A'(x).

Prog

(PARI) {a(n)=local(G=x); if(n<0, 0, if(n<=1, 1, G=x+sum(m=2, n, a(m-1)*x^m/(m-1)!)+x^2*O(x^n); n!*polcoeff(subst(G, x, subst(G, x, G))-2*x*G', n+1)/(2*n-2)))}

Crossrefs

Cf. A193264.

Sequence in context: A349505 A052756 A349651 * A317277 A138457 A252821

Adjacent sequences: A193262 A193263 A193264 * A193266 A193267 A193268

Keyword

nonn

Author

Paul D. Hanna, Jul 20 2011

Status

approved