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 A142146 A PolyLog functional polynomial coefficient triangular sequence: p(x,n)=(-1)^(n + 1)*(4*x + x^2)^(n + 1)*PolyLog[ -n, 1 + 4*x + x^2]/(1 + 4*x + x^2). 0
 1, 2, 4, 1, 6, 24, 22, 8, 1, 24, 144, 260, 176, 62, 12, 1, 120, 960, 2640, 3120, 1846, 616, 126, 16, 1, 720, 7200, 26760, 47040, 43352, 23376, 7772, 1632, 222, 20, 1, 5040, 60480, 283920, 672000, 882336, 692160, 347152, 115680, 25806, 3800, 366, 24, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row sums are: {1, 7, 61, 679, 9445, 158095, 3088765, 68958295, 1731875605, 48328686175}. LINKS FORMULA p(x,n)=(-1)^(n + 1)*(4*x + x^2)^(n + 1)*PolyLog[ -n, 1 + 4*x + x^2]/(1 + 4*x + x^2); t(n,m)=corefficients(p(x,n)). EXAMPLE {1}, {2, 4, 1}, {6, 24, 22, 8, 1}, {24, 144, 260, 176, 62, 12, 1}, {120, 960, 2640, 3120, 1846, 616, 126, 16, 1}, {720, 7200, 26760, 47040, 43352, 23376, 7772, 1632, 222, 20, 1}, {5040, 60480, 283920, 672000, 882336, 692160, 347152, 115680, 25806, 3800, 366, 24, 1}, {40320, 564480, 3205440, 9596160, 16690464, 17898048, 12504368, 5939584, 1972216, 462544, 75716, 8336, 590, 28, 1}, {362880, 5806080, 38707200, 140555520, 307308960, 427351680, 395017440, 252562560, 115055176, 38059712, 9226768, 1635344, 207430, 17864, 958, 32, 1}, {3628800, 65318400, 500169600, 2138572800, 5660202240, 9788567040, 11491935360, 9475050240, 5648068592, 2487777248, 820929560, 204235072, 38286104, 5359312, 546092, 38080, 1598, 36, 1} MATHEMATICA Clear[p, x, n, m]; p[x_, n_] = (-1)^(n + 1)*(4*x + x^2)^(n + 1)*PolyLog[ -n, 1 + 4*x + x^2]/(1 + 4*x + x^2); Table[FullSimplify[Expand[p[x, n]]], {n, 1, 10}]; Table[CoefficientList[FullSimplify[Expand[p[x, n]]], x], {n, 1, 10}]; Flatten[%] CROSSREFS Cf. A008292, A123125. Sequence in context: A021009 A137478 A089087 * A143350 A119303 A207610 Adjacent sequences:  A142143 A142144 A142145 * A142147 A142148 A142149 KEYWORD nonn,uned AUTHOR Roger L. Bagula and Gary W. Adamson, Sep 15 2008 STATUS approved

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