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 A243585 Expansion of log'(C(C(x)-1)-1), C(x)=(1-sqrt(1-4*x))/(2*x). 1
 1, 4, 20, 106, 580, 3244, 18446, 106250, 618340, 3628600, 21438820, 127377980, 760346350, 4556473276, 27396081950, 165189725326, 998492094244, 6048338850560, 36706629690824, 223139239595840, 1358475322091620 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G.-S. Cheon, H. Kim, L. W. Shapiro, Mutation effects in ordered trees, arXiv preprint arXiv:1410.1249, 2014 (see page 6). FORMULA a(n) = sum(k=0..n, binomial(2*k,k)*binomial(2*n,n-k)). a(n) ~ 5^(2*n+1/2) / (4^n * sqrt(3*Pi*n)). - Vaclav Kotesovec, Jun 08 2014 First column of A094527^2. 1 + x*exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + x + 4*x^2 + 18*x^3 + 86*x^4 + ... is the o.g.f. for A153294. - Peter Bala, Jul 21 2015 Conjecture: 2*n*(2*n-1)*(3*n-5)*a(n) +(-123*n^3+328*n^2-249*n+60)*a(n-1) +50*(n-1)*(2*n-3)*(3*n-2)*a(n-2)=0. - R. J. Mathar, Jun 14 2016 MATHEMATICA CoefficientList[Series[1/(Sqrt[(1-4*x)*(2*Sqrt[1-4*x]+5*x-2)/x]), {x, 0, 20}], x] (* Vaclav Kotesovec, Jun 08 2014 *) PROG (Maxima) a(n):=sum(binomial(2*k, k)*binomial(2*n, n-k), k, 0, n); CROSSREFS Cf. A000108, A094527, A153294. Sequence in context: A254537 A135159 A190724 * A263965 A265084 A321111 Adjacent sequences:  A243582 A243583 A243584 * A243586 A243587 A243588 KEYWORD nonn AUTHOR Vladimir Kruchinin, Jun 07 2014 STATUS approved

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Last modified February 21 15:11 EST 2019. Contains 320374 sequences. (Running on oeis4.)