cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

R. J. Mathar, Oct 01 2012

Keywords

Examples

			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 +...
		

Crossrefs

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

Programs

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

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