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 A154989 Symmetrical triangle sequence from polynomials: q(x,n)=(-1)^n*(Sum[(k + 1)^n*x^k/k, {k, 1, Infinity}] + Log[1 - x])*(x - 1)^n/x; p(x,n)=q(x,n)+x^n*q(1/x,n). 0
 2, 1, 1, 10, -16, 10, 11, -5, -5, 11, 36, -58, 92, -58, 36, 57, 21, 42, 42, 21, 57, 134, 156, 618, -376, 618, 156, 134, 247, 1303, 2529, 961, 961, 2529, 1303, 247, 520, 5162, 17524, 12646, 8936, 12646, 17524, 5162, 520, 1013, 19393, 99880, 153472, 89122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row sums are: 2*n!; {2, 2, 4, 12, 48, 240, 1440, 10080, 80640, 725760,...} LINKS FORMULA q(x,n)=(-1)^n*(Sum[(k + 1)^n*x^k/k, {k, 1, Infinity}] + Log[1 - x])*(x - 1)^n/x; p(x,n)=q(x,n)+x^n*q(1/x,n); t(n,m)=coefficients(p(x,n)). EXAMPLE {2}, {1, 1}, {10, -16, 10}, {11, -5, -5, 11}, {36, -58, 92, -58, 36}, {57, 21, 42, 42, 21, 57}, {134, 156, 618, -376, 618, 156, 134}, {247, 1303, 2529, 961, 961, 2529, 1303, 247}, {520, 5162, 17524, 12646, 8936, 12646, 17524, 5162, 520}, {1013, 19393, 99880, 153472, 89122, 89122, 153472, 99880, 19393, 1013} MATHEMATICA Clear[p, x, n]; p[x_, n_] = (-1)^n*(Sum[(k + 1)^n*x^k/k, {k, 1, Infinity}] + Log[1 - x])*(x - 1)^n/x; Table[FullSimplify[ExpandAll[p[x, n]]], {n, 1, 10}]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x] + Reverse[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]], {n, 1, 10}]; Flatten[%] CROSSREFS Sequence in context: A153731 A262226 A298158 * A064307 A165883 A260950 Adjacent sequences:  A154986 A154987 A154988 * A154990 A154991 A154992 KEYWORD uned,sign AUTHOR Roger L. Bagula, Jan 18 2009 STATUS approved

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Last modified October 17 04:09 EDT 2019. Contains 328106 sequences. (Running on oeis4.)