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A129086
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Coefficients of solution to A(x)= (1 +x*A(x)^2)* (1-3*x)/ (1-2*x)^2.
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0
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1, 2, 5, 14, 42, 133, 443, 1552, 5716, 22068, 88830, 370209, 1585841, 6936459, 30813483, 138445492, 627256282, 2859652414, 13099023380, 60225071992, 277729496928, 1283986487874, 5948991719082, 27616185153765
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OFFSET
| 0,2
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FORMULA
| Hankel transform of a(n) is A006720(n+3).
G.f. A(x) satisfies 0= f(x, A(x)) where f(u, v)= (v-1) +(3 -4*v -v^2)*u +(4*v +3*v^2)* u^2.
Let s(n)= A006769(n). Then 0= f( s(n+4)* s(n+6)/( s(n)* s(n+10)), -s(n)* s(n+7)/( s(n+3)* s(n+4)) ) where f(u, v)= (v-1) +(3 -4*v -v^2)*u +(4*v +3*v^2)* u^2.
G.f.: ((1 -2*x)^2 -sqrt((1 -4*x)* (1 -8*x +16*x^2 -4*x^3) ))/(2*x* (1 -3*x)).
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PROG
| (PARI) {a(n)= if(n<0, 0, polcoeff( ((1 -2*x)^2 -sqrt((1 -4*x)* (1 -8*x +16*x^2 -4*x^3) +x^2*O(x^n))) /(2*x* (1 -3*x)), n))}
(PARI) {a(n)= local(A); if(n<0, 0, A= 1+O(x); for(k= 1, n, A= (1+x*A^2)* (1-3*x)/ (1-2*x)^2 ); polcoeff(A, n))}
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CROSSREFS
| Sequence in context: A162748 A061815 A202061 * A035052 A148330 A149876
Adjacent sequences: A129083 A129084 A129085 * A129087 A129088 A129089
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Mar 29 2007
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