|
| |
|
|
A049136
|
|
Revert transform of (1 - 3x + x^3)/(1 - 2x - 2x^2).
|
|
0
|
|
|
|
1, 1, 2, 6, 22, 90, 392, 1775, 8252, 39114, 188220, 916920, 4512880, 22406488, 112092264, 564474555, 2859167178, 14557198500, 74459570756, 382441401734, 1971683051152, 10199692593804, 52927874586704, 275432533945182
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
LINKS
|
|
|
|
FORMULA
|
Recurrence: 81*(n-2)*(n-1)*n*(2016*n^4 - 11424*n^3 - 46810*n^2 + 395773*n - 620517)*a(n) = 54*(n-2)*(n-1)*(32256*n^5 - 231168*n^4 - 544672*n^3 + 8226740*n^2 - 22221907*n + 18224505)*a(n-1) - 12*(n-2)*(471744*n^6 - 4560192*n^5 - 1059012*n^4 + 160656726*n^3 - 725097457*n^2 + 1289426626*n - 830096175)*a(n-2) + 24*(233856*n^7 - 3079104*n^6 + 6489976*n^5 + 96147244*n^4 - 733225467*n^3 + 2201910978*n^2 - 3131108227*n + 1741444400)*a(n-3) + 16*(n-4)*(14112*n^6 - 150528*n^5 - 79702*n^4 + 7934357*n^3 - 43412159*n^2 + 93807595*n - 72346950)*a(n-4) + 192*(n-5)*(n-4)*(2*n - 11)*(2016*n^4 - 3360*n^3 - 68986*n^2 + 275945*n - 280962)*a(n-5). - Vaclav Kotesovec, Jan 02 2021
a(n) ~ 3^(n - 1/2) * 4^(n-1) * sqrt(6 - sqrt(3*(3*2^(2/3) - 2 - 2^(4/3))) - sqrt(3*(-4 + 2^(4/3) - 3*2^(2/3) + 4*sqrt(3/(-2 - 2^(4/3) + 3*2^(2/3)))))) / (sqrt(Pi) * n^(3/2) * (2 + (-1 + sqrt(1 + 2^(1/3) + 2^(2/3)) - sqrt(2 - 2^(1/3) - 2^(2/3) + 2/sqrt(1 + 2^(1/3) + 2^(2/3))))^3)^n). - Vaclav Kotesovec, Jan 02 2021
|
|
|
MATHEMATICA
|
Rest[CoefficientList[InverseSeries[Series[x*(1 - 3x + x^3)/(1 - 2x - 2x^2), {x, 0, 40}], x], x]] (* Vaclav Kotesovec, Jan 02 2021 *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
