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 A049140 Revert transform of 1 - x - x^3. 7
 1, 1, 2, 6, 20, 70, 256, 969, 3762, 14894, 59904, 244088, 1005452, 4180096, 17516936, 73913705, 313774854, 1339162028, 5742691704, 24731501410, 106919054880, 463844340060, 2018673093000, 8810852089650, 38558866555248 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Series reversion of x-x^2-x^4. - Joerg Arndt, May 24 2011 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..100, format errors corrected by Vaclav Kotesovec, Aug 07 2013 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 659 Vladimir Kruchinin, The method for obtaining expressions for coefficients of reverse generating functions, arXiv:1211.3244 [math.CO], 2012. Elżbieta Liszewska, Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019. FORMULA a(n) = sum(j=0..(n-1)/2, binomial(n-2*j-1,j)*binomial(2*n-2*j-2,n-1))/n. - Vladimir Kruchinin, May 24 2011 Conjecture: 31*n*(n-1)*(n-2)*(140*n-383)*a(n) -8*(n-1)*(n-2)*(2800*n^2 -11860*n+11583)*a(n-1) +4*(n-2)*(4480*n^3-30176*n^2+66916*n-48753)*a(n-2) -8*(4*n-11)*(4*n-13)*(140*n-243)*(2*n-5)*a(n-3) = 0. - R. J. Mathar, Sep 29 2012 MATHEMATICA CoefficientList[1/x InverseSeries[x*(1-x-x^3) + O[x]^26], x] (* Jean-François Alcover, Jul 20 2018 *) PROG (Maxima) a(n):=sum(binomial(n-2*j-1, j)*binomial(2*n-2*j-2, n-1), j, 0, (n-1)/2)/n; /* Vladimir Kruchinin, May 24 2011 */ (PARI) Vec(serreverse(x*(1-x-x^3+O(x^66)))) /* Joerg Arndt, May 24 2011 */ CROSSREFS Sequence in context: A192540 A185202 A340891 * A092413 A151285 A150126 Adjacent sequences:  A049137 A049138 A049139 * A049141 A049142 A049143 KEYWORD nonn AUTHOR STATUS approved

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Last modified September 21 07:10 EDT 2021. Contains 347596 sequences. (Running on oeis4.)