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A063033 Reversion of y - y^2 + y^4. 5
0, 1, 1, 2, 4, 8, 14, 16, -21, -242, -1166, -4472, -15132, -46508, -130016, -323000, -660535, -786714, 1789952, 18546464, 93845290, 380532240, 1355983860, 4363436280, 12688926510, 32530717752, 67666586472, 76255301640, -240266135872 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
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} (-1)^j*binomial(n-2*j-1, j)*binomial(2*n-2*j-2, n-1)/n, a(0)=0. - Vladimir Kruchinin, Oct 11 2011
D-finite with recurrence 391*n*(n-1)*(n-2)*a(n) -8*(n-1)*(n-2)*(203*n -132)*a(n-1) -4*(n-2)*(224*n^2 -2816*n +5697)*a(n-2) +8*(928*n^3 -7920*n^2 +22682*n-21915)*a(n-3) +192*(4*n-15) *(2*n-7)*(4*n-17)*a(n-4)=0, n-4>=1 - R. J. Mathar, Mar 24 2023
MATHEMATICA
CoefficientList[InverseSeries[Series[y - y^2 + y^4, {y, 0, 30}], x], x]
PROG
(Maxima)
a(n):=sum((-1)^j*binomial(n-2*j-1, j)*binomial(2*n-2*j-2, n-1), j, 0, (n-1)/2)/n; /* Vladimir Kruchinin, Oct 11 2011 */
(PARI) concat(0, Vec(serreverse(y - y^2 + y^4 + O(y^10)))) \\ Michel Marcus, Jun 28 2018
CROSSREFS
Sequence in context: A076380 A370840 A049133 * A128309 A074202 A086303
KEYWORD
sign,easy
AUTHOR
Olivier Gérard, Jul 05 2001
STATUS
approved

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Last modified June 19 19:59 EDT 2024. Contains 373507 sequences. (Running on oeis4.)