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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. 2
1, 1, 4, 17, 106, 796, 7176, 75057, 894100, 11946906, 176939192, 2876683340, 50931297912, 975391344376, 20090039762944, 442830738561585, 10400937450758286, 259318357362882148, 6839990934297006668 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

Table of n, a(n) for n=1..19.

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).

EXAMPLE

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 +...

PROG

(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)}

CROSSREFS

Cf. A122938; related tables: A122941, A122888.

Sequence in context: A091635 A127676 A232211 * A077386 A209903 A004140

Adjacent sequences:  A122937 A122938 A122939 * A122941 A122942 A122943

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 25 2006

STATUS

approved

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Last modified December 9 16:22 EST 2016. Contains 278985 sequences.