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 A168357 Self-convolution of A006664, which is the number of irreducible systems of meanders. 3
 1, 2, 5, 20, 112, 768, 5984, 50856, 460180, 4366076, 42988488, 436066232, 4532973676, 48095557700, 519247705968, 5690272928520, 63172884082028, 709373555125356, 8046263496489260, 92089662771965492, 1062482514810065752 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..20. FORMULA G.f.: A(x) = x/Series_Reversion(x*F(x)^2) where F(x) = g.f. of A001246, which is the squares of Catalan numbers. G.f.: A(x) = F(x/A(x))^2 where A(x*F(x)^2) = F(x)^2 where F(x) = g.f. of A001246. EXAMPLE G.f.: A(x) = 1 + 2*x + 5*x^2 + 20*x^3 + 112*x^4 + 768*x^5 +... A(x)^(1/2) = 1 + x + 2*x^2 + 8*x^3 + 46*x^4 + 322*x^5 + 2546*x^6 +...+ A006664(n)*x^n +... G.f. satisfies: A(x*F(x)^2) = F(x)^2 where F(x) = g.f. of A001246: F(x) = 1 + x + 4*x^2 + 25*x^3 + 196*x^4 + 1764*x^5 + 17424*x^6 +...+ A000108(n)^2*x^n +... F(x)^2 = 1 + 2*x + 9*x^2 + 58*x^3 + 458*x^4 + 4120*x^5 + 40569*x^6 +...+ A168358(n)*x^n +... PROG (PARI) {a(n)=local(C_2=vector(n+1, m, (binomial(2*m-2, m-1)/m)^2)); polcoeff(x/serreverse(x*Ser(C_2)^2), n)} CROSSREFS Cf. A168358, A168344, A001246, A006664, A000108. Sequence in context: A019536 A129949 A127065 * A052850 A000130 A288841 Adjacent sequences: A168354 A168355 A168356 * A168358 A168359 A168360 KEYWORD nonn AUTHOR Paul D. Hanna, Nov 23 2009 STATUS approved

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Last modified November 30 23:40 EST 2023. Contains 367464 sequences. (Running on oeis4.)