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 A063028 Reversion of x - x^2 + x^5. 2
 0, 1, 1, 2, 5, 13, 35, 96, 264, 720, 1925, 4966, 12038, 25907, 41310, -5168, -468996, -2982240, -14350320, -61334790, -244951840, -934684465, -3447083370, -12365767620, -43304717625, -148314737961, -497033803314, -1628721662260, -5208556347700 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS For the reversion of x - a*x^2 - b*x^5 (a!=0, b!=0) we have a(n) = Sum_{j=0..floor((n-1)/3)} a^(n-4*j-1)*b^j*binomial(n-3*j-1, j)*binomial(2*n-3*j-2, n-1)/n, n > 0. - Vladimir Kruchinin, May 28 2011 Obeys a 7-term hypergeometric recurrence with 4th-order polynomial coefficients. - R. J. Mathar, Nov 16 2012 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..125 Vladimir Kruchinin, The method for obtaining expressions for coefficients of reverse generating functions, arXiv:1211.3244 [math.CO], 2012. FORMULA a(n) = Sum_{j=0..floor((n-1)/3)} (-1)^j*binomial(n-3*j-1, j)*binomial(2*n-3*j-2, n-1)/n, n > 0, a(0)=0. - Vladimir Kruchinin, May 28 2011 MATHEMATICA CoefficientList[InverseSeries[Series[y - y^2 + y^5, {y, 0, 30}], x], x] PROG (Maxima) a(n):=sum((-1)^j*binomial(n-3*j-1, j)*binomial(2*n-3*j-2, n-1), j, 0, (n-1)/3)/n; /* Vladimir Kruchinin, May 28 2011 */ (PARI) x='x+O('x^66); /* that many terms */ Vec(serreverse(x-x^2+x^5)) /* show terms */ /* Joerg Arndt, May 28 2011 */ CROSSREFS Sequence in context: A227045 A007075 A000107 * A085810 A235611 A005773 Adjacent sequences:  A063025 A063026 A063027 * A063029 A063030 A063031 KEYWORD sign,easy AUTHOR Olivier Gérard, Jul 05 2001 STATUS approved

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Last modified May 27 04:00 EDT 2019. Contains 323597 sequences. (Running on oeis4.)