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A168592
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G.f.: exp( Sum_{n>=1} A082758(n)*x^n/n ), where A082758(n) = sum of the squares of the trinomial coefficients in row n of triangle A027907.
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4
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1, 3, 14, 80, 509, 3459, 24579, 180389, 1356743, 10402493, 81004516, 638886082, 5093081983, 40971735401, 332187974718, 2711668091448, 22267979870143, 183830653156341, 1524747465249750, 12700172705956876, 106187411693668179
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..20.
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FORMULA
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G.f.: A(x) = (1/x)*Series_Reversion[x*(1-x)^2/((1+x)^2*(1-x+x^2))].
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EXAMPLE
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G.f.: A(x) = 1 + 3*x + 14*x^2 + 80*x^3 + 509*x^4 + 3459*x^5 +...
log(A(x)) = 3*x + 19*x^2/2 + 141*x^3/3 + 1107*x^4/4 + 8953*x^5/5 +...+ A082758(n)*x^n/n +...
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PROG
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(PARI) {a(n)=if(n==0, 1, polcoeff(exp(sum(m=1, n, sum(k=0, 2*m, polcoeff((1+x+x^2)^m, k)^2)*x^m/m) +x*O(x^n)), n))}
(PARI) {a(n)=polcoeff(1/x*serreverse(x*(1-x)^2/((1+x)^2*(1-x+x^2)+x*O(x^n))), n)}
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CROSSREFS
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Cf. A168590, A168593, A082758, A027907, A168595.
Sequence in context: A020089 A218677 A027614 * A121873 A107596 A212391
Adjacent sequences: A168589 A168590 A168591 * A168593 A168594 A168595
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Dec 01 2009
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STATUS
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approved
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