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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..(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

LINKS

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

FORMULA

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]

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; [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 */

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 February 25 03:06 EST 2018. Contains 299630 sequences. (Running on oeis4.)