A049137 Revert transform of (1 - x - 4x^2 + x^3)/(1 - 4x^2 - 2x^3).

1, 1, 2, 6, 22, 88, 370, 1607, 7150, 32418, 149246, 695840, 3278942, 15591708, 74721660, 360540041, 1750069638, 8539926158, 41869742140, 206149706634, 1018875856490, 5053136206216, 25140141786040, 125436643981858

Offset

1,3

Links

Table of n, a(n) for n=1..24.

Index entries for reversions of series

Formula

Recurrence: 321*(n-2)*(n-1)*n*(11716537004*n^6 - 256139830260*n^5 + 2199943631138*n^4 - 9272371637469*n^3 + 19116132146402*n^2 - 15163838813733*n - 669010625046)*a(n) = 4*(n-2)*(n-1)*(6479244963212*n^7 - 151364193578598*n^6 + 1421811753982661*n^5 - 6810191796796971*n^4 + 17172543811195145*n^3 - 20186831623003335*n^2 + 4897077484745637*n + 5649967369355490)*a(n-1) - 12*(n-2)*(1769197087604*n^8 - 45753902719676*n^7 + 479586278527652*n^6 - 2568896159541686*n^5 + 7031222766810740*n^4 - 6685836601641683*n^3 - 11235982549272486*n^2 + 32319115762876365*n - 21761945647011090)*a(n-2) - 8*(8213292439804*n^9 - 241153714310790*n^8 + 3032643370590186*n^7 - 21276065588956767*n^6 + 90531673786295427*n^5 - 235949055911851095*n^4 + 354021249185228942*n^3 - 237985821515128407*n^2 - 34325500885650000*n + 97361546658986700)*a(n-3) + 16*(n-5)*(3315779972132*n^8 - 85750691852108*n^7 + 911547726333299*n^6 - 5064777807270668*n^5 + 15076816509533129*n^4 - 19498959416747735*n^3 - 8610001510445877*n^2 + 51577423574723568*n - 40011852899821860)*a(n-4) + 16*(n-6)*(n-5)*(2765102732944*n^7 - 59066448574888*n^6 + 500875625526064*n^5 - 2101319376996559*n^4 + 4256906007585436*n^3 - 2478825639623695*n^2 - 3975918505964292*n + 4810914782806932)*a(n-5) - 592*(n-7)*(n-6)*(n-5)*(11716537004*n^6 - 185840608236*n^5 + 1094992534898*n^4 - 2799664675437*n^3 + 2113028773283*n^2 + 2840685161940*n - 4033568591964)*a(n-6). - Vaclav Kotesovec, Jan 02 2021

Mathematica

Rest[CoefficientList[InverseSeries[Series[x*(1 - x - 4x^2 + x^3)/(1 - 4x^2 - 2x^3), {x, 0, 40}], x], x]] (* Vaclav Kotesovec, Jan 02 2021 *)

Crossrefs

Sequence in context: A049135 A049127 A199481 * A287223 A365246 A333080

Adjacent sequences: A049134 A049135 A049136 * A049138 A049139 A049140

Keyword

nonn

Author

Olivier Gérard

Status

approved