The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A140055 E.g.f.: A(x) = G(G(x)) where G(x) = x*exp(A(x)) such that G( x*exp(-G(x)) ) = x and G(x) is the e.g.f. of A140054. 3
 1, 4, 42, 764, 20400, 731862, 33397168, 1867950856, 124680486816, 9733666171850, 874978919826264, 89437471672859532, 10289414670501314608, 1320997962702267801070, 187894667581541881127640, 29426125555003596239544848, 5046809953516305090792395328 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..282 EXAMPLE E.g.f.: A(x) = x + 4*x^2/2! + 42*x^3/3! + 764*x^4/4! + 20400*x^5/5! +... x*exp(A(x)) = x + 2*x^2/2! + 15*x^3/3! + 220*x^4/4! + 5025*x^5/5! +... where G(x) = x*exp(A(x)) satisfies G(G(x)) = A(x). MAPLE b:= proc(n, k) option remember; `if`(n=0, 1/k, add(k* b(j-1, j)*j*b(n-j, k)*binomial(n-1, j-1), j=1..n)) end: a:= n-> b(n\$2): seq(a(n), n=1..20); # Alois P. Heinz, Aug 21 2019 MATHEMATICA m = 20; G[_] = 0; Do[G[x_] = x Exp[G[G[x]]] + O[x]^(m+1) // Normal, {m}]; CoefficientList[G[G[x]]/x + O[x]^m, x]*Range[m]! (* Jean-François Alcover, Oct 14 2019 *) PROG (PARI) {a(n)=local(A=x); for(i=0, n, A=x*exp(subst(A, x, A+x*O(x^n)))); n!*polcoeff(subst(A, x, A), n)} CROSSREFS Cf. A140054 (x*exp(A(x))). Sequence in context: A074768 A295763 A266526 * A221096 A179499 A268567 Adjacent sequences: A140052 A140053 A140054 * A140056 A140057 A140058 KEYWORD nonn AUTHOR Paul D. Hanna, May 03 2008 STATUS approved

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

Last modified September 13 07:00 EDT 2024. Contains 375865 sequences. (Running on oeis4.)