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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-Fran├žois 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

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Last modified August 17 08:02 EDT 2022. Contains 356184 sequences. (Running on oeis4.)