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 A154854 Symmetrical triangular sequence: p(x,n) =((-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(4*m + 3)^ n*x^m, {m, 0, Infinity}] - (-1)^(n + 1)*(x - 1)^(n + 1)* Sum[(4*m + 1)^n*x^m, {m, 0, Infinity}])/2. 0
 1, -1, 4, 0, -4, 13, 57, -57, -13, 40, 688, 0, -688, -40, 121, 6115, 11770, -11770, -6115, -121, 364, 48464, 270620, 0, -270620, -48464, -364, 1093, 363965, 4401033, 5613265, -5613265, -4401033, -363965, -1093, 3280, 2657568, 61590368 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row sums are zero. LINKS FORMULA p(x,n) = ((-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(4*m + 3)^ n*x^m, {m, 0, Infinity}] - (-1)^(n + 1)*(x - 1)^(n + 1)* Sum[(4*m + 1)^n*x^m, {m, 0, Infinity}])/2; t(n,m)=coefficients(p(x,n)) EXAMPLE {}, {1, -1}, {4, 0, -4}, {13, 57, -57, -13}, {40, 688, 0, -688, -40}, {121, 6115, 11770, -11770, -6115, -121}, {364, 48464, 270620, 0, -270620, -48464, -364}, {1093, 363965, 4401033, 5613265, -5613265, -4401033, -363965, -1093}, {3280, 2657568, 61590368, 199134880, 0, -199134880, -61590368, -2657568, -3280}, {9841, 19101831, 793704036, 4929623916, 4890510366, -4890510366, -4929623916, -793704036, -19101831, -9841}, {29524, 136030048, 9727040988, 103412071488, 239084539848, 0, -239084539848, -103412071488, -9727040988, -136030048, -29524} MATHEMATICA Clear[p]; p[x_, n_] = ((-1)^(n + 1)*(x - 1)^(n + 1)*Sum[(4*m + 3)^ n*x^m, {m, 0, Infinity}] - (-1)^(n + 1)*(x - 1)^(n + 1)* Sum[(4*m + 1)^n*x^m, {m, 0, Infinity}])/2; Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A209134 A281297 A058536 * A151672 A058493 A112149 Adjacent sequences:  A154851 A154852 A154853 * A154855 A154856 A154857 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Jan 16 2009 STATUS approved

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Last modified October 22 19:53 EDT 2019. Contains 328319 sequences. (Running on oeis4.)