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A142146
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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).
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0
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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
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OFFSET
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1,2
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COMMENTS
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Row sums are:
{1, 7, 61, 679, 9445, 158095, 3088765, 68958295, 1731875605, 48328686175}.
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LINKS
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FORMULA
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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)).
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EXAMPLE
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{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}
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MATHEMATICA
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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[%]
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CROSSREFS
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KEYWORD
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nonn,uned
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AUTHOR
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STATUS
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approved
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