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A063028
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Reversion of x - x^2 + x^5.
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2
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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
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OFFSET
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0,4
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COMMENTS
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For the reversion of x - a*x^2 - b*x^5 (a!=0, b!=0) we have a(n)=sum(j=0..(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. [From Vladimir Kruchinin, May 28 2011]
Obeys a 7-term hypergeometric recurrence with 4th order polynomial coefficients. - R. J. Mathar, Nov 16 2012
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..125
Index entries for reversions of series
Vladimir Kruchinin, The method for obtaining expressions for coefficients of reverse generating functions, arXiv:1211.3244
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FORMULA
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a(n)=sum(j=0..(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. [From Vladimir Kruchinin, May 28 2011]
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MATHEMATICA
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CoefficientList[InverseSeries[Series[y - y^2 + y^5, {y, 0, 30}], x], x]
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PROG
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(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; [From 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 */
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CROSSREFS
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Sequence in context: A057960 A007075 A000107 * A085810 A005773 A022855
Adjacent sequences: A063025 A063026 A063027 * A063029 A063030 A063031
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KEYWORD
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sign,easy
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AUTHOR
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Olivier Gérard, Jul 05 2001.
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STATUS
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approved
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