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Search: id:A122938
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| A122938 |
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G.f. A(x) satisfies: A(x+x^2) = A(x)^2/(1+x). |
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+0
3
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| 1, 1, 1, 2, 6, 27, 160, 1189, 10600, 110161, 1306629, 17408293, 257299241, 4177017722, 73872560359, 1413560616317, 29096001945172, 641010535303531, 15049350893772391, 375084409475304164, 9890697492431533299
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Self-convolution equals A122939. See A122888 for the table of self-compositions of x+x^2.
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FORMULA
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G.f.: A(x) = Product_{n>=0} (1 + F_n(x) )^(1/2^(n+1)) where F_0(x)=x, F_{n+1}(x)=F_n(x+x^2); a product that involves the n-th self-compositions of x+x^2.
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EXAMPLE
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G.f.: A(x) = (1 + x)^(1/2) * (1 + x+x^2)^(1/4) * (1 + x+2x^2+2x^3+x^4)^(1/8) * (1 + x+3x^2+6x^3+9x^4+10x^5+8x^6+4x^7+x^8)^(1/16) *...
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PROGRAM
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=-A+2*sqrt((1+x)*subst(A, x, x+x^2+x*O(x^n)))); polcoeff(A, n)}
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CROSSREFS
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Cf. A122939 (A^2), A122940 (log), A122941-A122945; A122888 (table).
Sequence in context: A058133 A009308 A032186 this_sequence A058712 A070076 A130455
Adjacent sequences: A122935 A122936 A122937 this_sequence A122939 A122940 A122941
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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 21 2006
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