A122940 L.g.f.: A(x) satisfies: A(x+x^2) = 2*A(x) - log(1+x) with A(0)=0; thus A(x) = log(B(x)), where B(x) is g.f. of A122938.

1, 1, 4, 17, 106, 796, 7176, 75057, 894100, 11946906, 176939192, 2876683340, 50931297912, 975391344376, 20090039762944, 442830738561585, 10400937450758286, 259318357362882148, 6839990934297006668

Offset: 1

Author

Paul D. Hanna, Sep 25 2006

Keywords

• nonn

Comments

a(n) = n * Sum_{k=0..n-1} (-1)^(n-k-1)*A122941(n-k,k)/(n-k).

Examples

			To illustrate A(x+x^2) = 2*A(x) - log(1+x):
A(x) = x + 1*x^2/2 + 4*x^3/3 + 17*x^4/4 + 106*x^5/5 + 796*x^6/6 +...
A(x+x^2) = x + 3*x^2/2 + 7*x^3/3 + 35*x^4/4 + 211*x^5/5 + 1593*x^6/6 +...
		

Crossrefs

Cf. A122938; related tables: A122941, A122888.

Programs

PARI

{a(n)=local(A=x+x*O(x^n)); for(i=0,n,A=-A+subst(A,x,x+x^2)+log(1+x+x*O(x^n)));n*polcoeff(A,n)}

Formula

L.g.f.: A(x) = Sum_{n>=1} a(n)*x^n/n = Sum_{n>=0} log(1 + F_n(x))/2^(n+1) where F_0(x)=x, F_{n+1}(x) = F_n(x+x^2); a sum involving self-compositions of x+x^2 (cf. A122888).