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Search: id:A093126
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| A093126 |
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G.f.: A(x) = x/(1 - x - G001190(x^2)), where G001190 is the g.f. of A001190, the Wedderburn-Etherington numbers (binary rooted trees). |
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+0
1
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| 0, 1, 1, 2, 3, 6, 10, 19, 33, 62, 110, 204, 366, 675, 1219, 2239, 4059, 7439, 13518, 24737, 45018, 82304, 149924, 273929, 499290, 911902, 1662787, 3036105, 5537577, 10109364, 18441799, 33663239, 61416729, 112099746, 204536183, 373305550
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Not the same as A003237.
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FORMULA
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G.f. satisfies the following identities: A(x^2) = A(x)^2/(1+2*A(x)+2*A(x)^2); A(-x) = -A(x)/(1+2*A(x)); A(x)+A(-x) = -2*A(x)*A(-x); A(x)^2/(1+2*A(x)) = A(x^2)/(1-2*A(x^2)).
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EXAMPLE
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A(x) = x + x^2 + 2x^3 + 3x^4 + 6x^5 + 10x^6 + 19x^7 + 33x^8 + ... = x/(1-x -(x^2 + x^4 + x^6 + 2x^8 + 3x^10 + 11x^12 + 23x^14 + ...)).
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PROGRAM
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(PARI) {a(n)=local(A, u, v); if(n<0, 0, A=x; for(k=2, n, u=A+x*O(x^k); v=subst(u, x, x^2); A-=x^k*polcoeff(u^2 -v*(1+2*u+2*u^2), k+1)/2); polcoeff(A, n))}
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CROSSREFS
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Cf. A001190, A003237.
Sequence in context: A079959 A028495 A136752 this_sequence A003237 A026021 A123916
Adjacent sequences: A093123 A093124 A093125 this_sequence A093127 A093128 A093129
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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), Mar 23 2004
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