A217359 Series reversion of x+x^3+x^4.

1, 0, -1, -1, 3, 7, -8, -45, 0, 264, 273, -1365, -3192, 5508, 27132, -7752, -193743, -158631, 1177209, 2417415, -5673525, -23595585, 14488110, 187050435, 104481780, -1251127512, -2178989008, 6775504088, 23824892148, -23395134188, -204487059656, -57418615353, 1471227866951

Offset

1,5

Links

R. J. Mathar, Table of n, a(n) for n = 1..104

Formula

D-finite with recurrence 124*n*(n-1)*(n-2)*a(n) +(n-1)*(n-2)*(7*n-88)*a(n-1) +(n-2)*(870*n^2-3465*n+3347)*a(n-2) +(1243*n^3-9870*n^2+25869*n-22490)*a(n-3) +8*(4*n-15)*(2*n-7)*(4*n-17)*a(n-4) = 0.

Recurrence (order 3): 31*(n-2)*(n-1)*n*(15*n-41)*a(n) = (n-2)*(n-1)*(90*n^2 - 381*n + 400)*a(n-1) - (n-2)*(3285*n^3 - 22119*n^2 + 48706*n - 34960)*a(n-2) - 8*(2*n-5)*(4*n-13)*(4*n-11)*(15*n-26)*a(n-3). - Vaclav Kotesovec, Sep 10 2013

Lim sup n->infinity |a(n)|^(1/n) = 16/sqrt(31) = 2.8736848... - Vaclav Kotesovec, Sep 10 2013

Example

If y= x+x^3+x^4, then x=y -y^3 -y^4 +3*y^5 +7*y^6 -8*y^7 -45*y^8 +...

Mathematica

Rest[CoefficientList[InverseSeries[Series[x+x^3+x^4, {x, 0, 20}], x], x]] (* Vaclav Kotesovec, Sep 10 2013 *)

Crossrefs

Cf. A217358 (x-x^3-x^4).

Sequence in context: A281678 A118622 A101366 * A244338 A336045 A090458

Adjacent sequences: A217356 A217357 A217358 * A217360 A217361 A217362

Keyword

sign,easy

Author

R. J. Mathar, Oct 01 2012

Status

approved