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A049138
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Revert transform of (1 - 3x + 2x^2 + x^3)/(1 - 2x + 2x^3).
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0
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1, 1, 2, 6, 20, 70, 254, 947, 3604, 13936, 54574, 215914, 861454, 3461208, 13988932, 56821743, 231793334, 949033702, 3897956648, 16053912116, 66275614190, 274168532480, 1136192222288, 4715741791756, 19598263084654
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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: 23*(n-2)*(n-1)*n*(17172*n^6 - 423576*n^5 + 4356666*n^4 - 23917917*n^3 + 73913950*n^2 - 121852969*n + 83627530)*a(n) = 4*(n-2)*(n-1)*(1081836*n^7 - 28308042*n^6 + 315057411*n^5 - 1931263794*n^4 + 7030821771*n^3 - 15164709990*n^2 + 17878090855*n - 8840503650)*a(n-1) - 4*(n-2)*(3966732*n^8 - 113712984*n^7 + 1415715948*n^6 - 9998014698*n^5 + 43802809404*n^4 - 121878698873*n^3 + 210225001262*n^2 - 205376774691*n + 86927649480)*a(n-2) + 8*(2936412*n^9 - 94454586*n^8 + 1341241794*n^7 - 11038095603*n^6 + 58034133171*n^5 - 202174640931*n^4 + 466677806698*n^3 - 688129298199*n^2 + 587881625144*n - 221535308520)*a(n-3) - 16*(n-5)*(1184868*n^8 - 33966216*n^7 + 422624169*n^6 - 2983362075*n^5 + 13075866015*n^4 - 36449461159*n^3 + 63104412886*n^2 - 62005448370*n + 26439990552)*a(n-4) + 16*(n-6)*(n-5)*(618192*n^7 - 14939640*n^6 + 153479988*n^5 - 870020397*n^4 + 2941516152*n^3 - 5933206737*n^2 + 6606477556*n - 3125798560)*a(n-5) - 176*(n-7)*(n-6)*(n-5)*(17172*n^6 - 320544*n^5 + 2496366*n^4 - 10383573*n^3 + 24322015*n^2 - 30367004*n + 15720856)*a(n-6). - Vaclav Kotesovec, Jan 02 2021
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MATHEMATICA
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Rest[CoefficientList[InverseSeries[Series[x*(1 - 3x + 2x^2 + x^3)/(1 - 2x + 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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