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 A253256 G.f. satisfies: A(x) = (1 - x^3*A(x)^6) / (1 - x*A(x)^2)^2. 1
 1, 2, 11, 79, 647, 5727, 53367, 515802, 5123303, 51977485, 536320688, 5610909773, 59379328267, 634538481389, 6837466955193, 74210071037031, 810527496757335, 8901979424068377, 98253966680382102, 1089260346498608721, 12123804391067414676, 135427509933882292680, 1517725698030921469890 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Self-convolution yields A253255. LINKS FORMULA G.f. A(x) satisfies: (1) A(x) = exp( Sum_{n>=1} A168595(n)/2 * x^n/n ), where A168595(n) = Sum_{k=0..2*n} binomial(n,k)*trinomial(n,k). (2) A(x) = sqrt( (1/x)*Series_Reversion( x*(1-x)^4/(1-x^3)^2 ) ). (3) A(x) = sqrt( (1-x*A(x) - sqrt(1 - 6*x*A(x) - 3*x^2*A(x)^2)) / (2*x*(1+x*A(x))) ). EXAMPLE G.f.: A(x) = 1 + 2*x + 11*x^2 + 79*x^3 + 647*x^4 + 5727*x^5 + 53367*x^6 +... where A(x) = (1 - x^3*A(x)^6) / (1 - x*A(x)^2)^2. The logarithm begins: log(A(x)) = 2*x + 18*x^2 + 179*x^3 + 1874*x^4 + 20202*x^5 + 221943*x^6 + 2470827*x^7/7 +...+ A168595(n)/2*x^n/n +... PROG (PARI) {a(n) = local(A=1); A = sqrt( (1/x)*serreverse( x*(1-x)^4/(1-x^3)^2 +x^2*O(x^n))); polcoeff(A, n)} for(n=0, 30, print1(a(n), ", ")) (PARI) {A168595(n) = sum(k=0, 2*n, binomial(2*n, k) * polcoeff((1+x+x^2)^n, k) )} {a(n) = local(A=1); A = exp( sum(k=1, n+1, A168595(k)/2 * x^k/k) +x*O(x^n)); polcoeff(A, n)} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A168595, A106228, A064641, A253255. Sequence in context: A094569 A151418 A154273 * A163203 A142722 A320095 Adjacent sequences:  A253253 A253254 A253255 * A253257 A253258 A253259 KEYWORD nonn AUTHOR Paul D. Hanna, May 31 2015 STATUS approved

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Last modified September 15 18:22 EDT 2019. Contains 327082 sequences. (Running on oeis4.)