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Search: id:A122940
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| A122940 |
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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. |
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+0
3
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| 1, 1, 4, 17, 106, 796, 7176, 75057, 894100, 11946906, 176939192, 2876683340, 50931297912, 975391344376, 20090039762944, 442830738561585, 10400937450758286, 259318357362882148, 6839990934297006668
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n) = n * Sum_{k=0..n-1} (-1)^(n-k-1)*A122941(n-k,k)/(n-k).
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FORMULA
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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).
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EXAMPLE
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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 +...
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PROGRAM
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(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)}
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CROSSREFS
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Cf. A122938; related tables: A122941, A122888.
Sequence in context: A128321 A091635 A127676 this_sequence A077386 A004140 A032115
Adjacent sequences: A122937 A122938 A122939 this_sequence A122941 A122942 A122943
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Sep 25 2006
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