The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A193265 E.g.f. A(x) = G(x)/x where G(x) satisfies: G(G(G(x))) = 2*x*G'(x) - G(x). 2
 1, 1, 6, 81, 1828, 59910, 2629800, 146775160, 10047085200, 821599116300, 78674552192800, 8684916065005620, 1091429676788178240, 154543476785542516360, 24445478524707259098240, 4288239906998845117572000, 829048705765475214447735040 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 3 00:59 EST 2021. Contains 349445 sequences. (Running on oeis4.)