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Search: id:A122939
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| A122939 |
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G.f. A(x) satisfies: A(x+x^2) = A(x)^2/(1+x)^2. |
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+0
2
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| 1, 2, 3, 6, 17, 70, 390, 2776, 24042, 244864, 2862185, 37715474, 552685976, 8910951840, 156709821779, 2984589501562, 61188398397436, 1343410717573876, 31445844702847347, 781689483100388326, 20564696601659697997
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Self-convolution of A122938. 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) 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 + x+x^2)^(1/2) * (1 + x+2x^2+2x^3+x^4)^(1/4) * (1 + x+3x^2+6x^3+9x^4+10x^5+8x^6+4x^7+x^8)^(1/8) *...
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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*(1+x)*sqrt(subst(A, x, x+x^2+x*O(x^n)))); polcoeff(A, n)}
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CROSSREFS
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Cf. A122938 (square-root), A122888 (table).
Adjacent sequences: A122936 A122937 A122938 this_sequence A122940 A122941 A122942
Sequence in context: A078344 A024498 A114491 this_sequence A003183 A131788 A080338
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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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