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.

1, 4, 42, 764, 20400, 731862, 33397168, 1867950856, 124680486816, 9733666171850, 874978919826264, 89437471672859532, 10289414670501314608, 1320997962702267801070, 187894667581541881127640, 29426125555003596239544848, 5046809953516305090792395328

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