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A049134
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Revert transform of (1 - 5x + 6x^2 - x^3)/(1 - 4x + 2x^2 + 2x^3).
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0
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1, 1, 2, 6, 22, 90, 394, 1805, 8538, 41344, 203790, 1018562, 5148110, 26261120, 135005708, 698686953, 3636870218, 19027686362, 100002510548, 527713256528, 2794955279330, 14852320704712, 79164310947304, 423126034866776
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OFFSET
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1,3
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LINKS
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FORMULA
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Recurrence: 49*(n-2)*(n-1)*n*(97276*n^6 - 3688284*n^5 + 57658918*n^4 - 479607669*n^3 + 2216546002*n^2 - 5330445909*n + 5131212282)*a(n) = 84*(n-2)*(n-1)*(875484*n^7 - 34507782*n^6 + 570495625*n^5 - 5153850896*n^4 + 27187400381*n^3 - 82564289080*n^2 + 131577203517*n - 83678026950)*a(n-1) - 4*(n-2)*(104960804*n^8 - 4399501652*n^7 + 78979914800*n^6 - 797238406844*n^5 + 4921740693398*n^4 - 18879733709831*n^3 + 43633751045376*n^2 - 55262650820391*n + 29263140459000)*a(n-2) + 8*(137061884*n^9 - 6224756286*n^8 + 123581488872*n^7 - 1414377109011*n^6 + 10261575676887*n^5 - 48731097765747*n^4 + 150804473709004*n^3 - 292120501382991*n^2 + 320306006672208*n - 150947753913720)*a(n-3) - 16*(n-5)*(81517288*n^8 - 3416851144*n^7 + 61807835563*n^6 - 634081949563*n^5 + 4021282083769*n^4 - 16034262690649*n^3 + 38962622750796*n^2 - 52327943564058*n + 29425007886408)*a(n-4) + 16*(n-6)*(n-5)*(38715848*n^7 - 1448579108*n^6 + 22955879084*n^5 - 201324959537*n^4 + 1047347662268*n^3 - 3190983086621*n^2 + 5195959692204*n - 3412537568496)*a(n-5) - 592*(n-7)*(n-6)*(n-5)*(97276*n^6 - 3104628*n^5 + 40676638*n^4 - 283909317*n^3 + 1088252803*n^2 - 2123399004*n + 1591772616)*a(n-6). - Vaclav Kotesovec, Jan 02 2021
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MATHEMATICA
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Rest[CoefficientList[InverseSeries[Series[x*(1 - 5x + 6x^2 - x^3)/(1 - 4x + 2x^2 + 2x^3), {x, 0, 40}], x], x]] (* Vaclav Kotesovec, Jan 02 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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