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 A176389 A symmetrical triangle of polynomial coefficients:p(x,n)=Sum[(1 + Binomial[n, m]*x)^m*(1 - Binomial[n, m]*x)^(n - m) + (x + Binomial[n, m])^m*(x - Binomial[n, m])^(n - m), {m, 0, n}] 0
 2, 2, 2, 1, 0, 1, 4, -12, -12, 4, 791, 0, -120, 0, 791, 6, 16260, -280, -280, 16260, 6, -41312053, 0, 364560, 0, 364560, 0, -41312053, 8, -3163111000, -5544, 7035000, 7035000, -5544, -3163111000, 8, 383801047294219, 0, -343384323744, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row sums are: {2, 4, 2, -16, 1462, 31972, -81894986, -6312163072, 766915589474990, 224370055225370444, -1400713126150624370808722,...}. LINKS Table of n, a(n) for n=0..39. FORMULA p(x,n)=Sum[(1 + Binomial[n, m]*x)^m*(1 - Binomial[n, m]*x)^(n - m) + (x + Binomial[n, m])^m*(x - Binomial[n, m])^(n - m), {m, 0, n}]; t(n,m)=coefficients(p(x,n)) EXAMPLE {2}, {2, 2}, {1, 0, 1}, {4, -12, -12, 4}, {791, 0, -120, 0, 791}, {6, 16260, -280, -280, 16260, 6}, {-41312053, 0, 364560, 0, 364560, 0, -41312053}, {8, -3163111000, -5544, 7035000, 7035000, -5544, -3163111000, 8}, {383801047294219, 0, -343384323744, 0, 263534040, 0, -343384323744, 0, 383801047294219}, {10, 112211416526896260, -102960, -26391294385680, 2380277592, 2380277592, -26391294385680, -102960, 112211416526896260, 10}, {-700414925359462889249761, 0, 58364418631721000040, 0, -2134481017154640, 0, -2134481017154640, 0, 58364418631721000040, 0, -700414925359462889249761} MATHEMATICA p[x_, n_] = Sum[(1 + Binomial[n, m]*x)^m*(1 - Binomial[n, m]*x)^(n - m) + (x + Binomial[n, m])^m*(x - Binomial[n, m])^(n - m), {m, 0, n}]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A246575 A357563 A112215 * A076451 A230536 A306257 Adjacent sequences: A176386 A176387 A176388 * A176390 A176391 A176392 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Apr 16 2010 STATUS approved

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Last modified February 25 16:57 EST 2024. Contains 370332 sequences. (Running on oeis4.)