A049141 Revert transform of (1 + x - 4x^2 - x^3)/(1 + 2x - 2x^2 - 2x^3).

1, 1, 2, 6, 20, 72, 270, 1049, 4176, 16962, 69990, 292608, 1236718, 5275724, 22685636, 98225447, 427888458, 1873979814, 8246535936, 36444747110, 161685649174, 719819353928, 3214805630688, 14399464322254, 64668729869542

Offset

1,3

Links

Table of n, a(n) for n=1..25.

Index entries for reversions of series

Formula

Recurrence: 321*(n-2)*(n-1)*n*(13132556180*n^6 - 319524181392*n^5 + 3193060117034*n^4 - 16778569684929*n^3 + 48903661204010*n^2 - 74972342495745*n + 47236617193374)*a(n) = 4*(n-2)*(n-1)*(2376992668580*n^7 - 61399365834822*n^6 + 662719125839483*n^5 - 3865276461360123*n^4 + 13107548627695403*n^3 - 25691751639299019*n^2 + 26688775958402049*n - 11137098037724910)*a(n-1) + 4*(n-2)*(12147614466500*n^8 - 344150325653600*n^7 + 4190412274017848*n^6 - 28646628057425120*n^5 + 120280372393857206*n^4 - 317687193530897519*n^3 + 515535425187033504*n^2 - 469996410791522169*n + 184291140349328490)*a(n-2) + 8*(1956750870820*n^9 - 62284734558558*n^8 + 867904877618364*n^7 - 6933649341787155*n^6 + 34920871152655959*n^5 - 114716612257282719*n^4 + 245181002719349738*n^3 - 327813694870574997*n^2 + 247964171632135308*n - 80524500563978460)*a(n-3) - 16*(n-5)*(1759762528120*n^8 - 49855290419008*n^7 + 605388788022973*n^6 - 4110725601489190*n^5 + 17049772633750663*n^4 - 44166616660419583*n^3 + 69668406864706761*n^2 - 61076567753896320*n + 22745476529228484)*a(n-4) + 16*(n-6)*(n-5)*(1234460280920*n^7 - 29418042910388*n^6 + 293583606173768*n^5 - 1588435888263095*n^4 + 5026017332226368*n^3 - 9289599488458571*n^2 + 9277035186704400*n - 3858169082650884)*a(n-5) - 592*(n-7)*(n-6)*(n-5)*(13132556180*n^6 - 240728844312*n^5 + 1792427552774*n^4 - 6938919907113*n^3 + 14728059380207*n^2 - 16247314244256*n + 7276034708532)*a(n-6). - Vaclav Kotesovec, Jan 02 2021

Mathematica

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

Crossrefs

Sequence in context: A244783 A216837 A192658 * A049129 A063376 A161168

Adjacent sequences: A049138 A049139 A049140 * A049142 A049143 A049144

Keyword

nonn

Author

Olivier Gérard

Status

approved