A063033 Reversion of y - y^2 + y^4.

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

Offset

0,4

Links

Michael De Vlieger, Table of n, a(n) for n = 0..800

Elżbieta Liszewska, Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.

Index entries for reversions of series

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

Adjacent sequences: A063030 A063031 A063032 * A063034 A063035 A063036

Keyword

sign,easy

Author

Olivier Gérard, Jul 05 2001

Status

approved