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 A063018 Reversion of x - x^2 - x^3 - x^4. 3
 0, 1, 1, 3, 11, 44, 189, 850, 3951, 18832, 91542, 452075, 2261753, 11439372, 58394014, 300455892, 1556636807, 8113709916, 42518000652, 223868503324, 1183764310960, 6283573101960, 33470346433605, 178850415320010 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS For the reversion of x - a*x^2 - b*x^3 - c*x^4 (a!=0, b!=0, c!=0) we have a(n) = Sum(k=1,n-1, (Sum(j=0..k, a^(-n+3*k-j+1) * b^(n-3*k+2*j-1) * c^(k-j) * binomial(j,n-3*k+2*j-1) * binomial(k,j) ) ) * binomial(n+k-1,n-1))/n, n>1, a(1)=1. - Vladimir Kruchinin, May 28 2011 G.f. (with offset 1) satisfies A(x) = 1 + x*A(x)^2 + x^2*A(x)^3. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..105 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(k=1..n-1, (Sum(j=0..k, binomial(j,n-3*k+2*j-1) * binomial(k,j))) * binomial(n+k-1,n-1))/n, n>1, a(1)=1, a(0)=0. - Vladimir Kruchinin, May 28 2011 MATHEMATICA CoefficientList[InverseSeries[Series[y - y^2 - y^3 - y^4, {y, 0, 30}], x], x] PROG (Maxima) a(n):=sum((sum(binomial(j, n-3*k+2*j-1)*binomial(k, j), j, 0, k))*binomial(n+k-1, n-1), k, 1, n-1)/n; \\ Vladimir Kruchinin, May 28 2011 (PARI) x='x+O('x^66); /* that many terms */ Vec(serreverse(x-x^2-x^3-x^4)) /* show terms */ /* Joerg Arndt, May 28 2011 */ CROSSREFS Cf. A001002 (reversion of y - y^2 - y^3). Sequence in context: A151106 A302186 A151107 * A293468 A151108 A256752 Adjacent sequences:  A063015 A063016 A063017 * A063019 A063020 A063021 KEYWORD nonn,easy AUTHOR Olivier Gérard, Jul 05 2001 STATUS approved

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Last modified December 15 14:37 EST 2019. Contains 329999 sequences. (Running on oeis4.)