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 A176664 A leading coefficient adjusted symmetrical triangle of polynomial coefficients based on:p(x,n)=Sum[k!*Binomial[x, k], {k, 0, n}] 0
 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -10, 17, -10, 1, 1, 10, -12, -12, 10, 1, 1, -115, 308, -391, 308, -115, 1, 1, 599, -1371, 769, 769, -1371, 599, 1, 1, -4448, 11838, -13503, 12219, -13503, 11838, -4448, 1, 1, 35864, -97529, 102186, -40525, -40525, 102186 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 COMMENTS Row sums are: {1, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7,...}. LINKS FORMULA p(x,n)=Sum[k!*Binomial[x, k], {k, 0, n}]; t(n,m)=coefficients(p(x,n))+reverse(coefficients(p(x,n)))-1 EXAMPLE {1}, {1, 1}, {1, -1, 1}, {1, -1, -1, 1}, {1, -10, 17, -10, 1}, {1, 10, -12, -12, 10, 1}, {1, -115, 308, -391, 308, -115, 1}, {1, 599, -1371, 769, 769, -1371, 599, 1}, {1, -4448, 11838, -13503, 12219, -13503, 11838, -4448, 1}, {1, 35864, -97529, 102186, -40525, -40525, 102186, -97529, 35864, 1}, {1, -327025, 929363, -1075211, 721544, -497351, 721544, -1075211, 929363, -327025, 1} MATHEMATICA Clear[p, x, n] p[x_, n_] := Sum[k!*Binomial[x, k], {k, 0, n}]; Table[CoefficientList[ExpandAll[p[x, n]], x] + Reverse[CoefficientList[ ExpandAll[p[x, n]], x]] - 1, {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A167331 A255531 A157159 * A256346 A079630 A175389 Adjacent sequences:  A176661 A176662 A176663 * A176665 A176666 A176667 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Apr 23 2010 STATUS approved

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Last modified July 20 05:43 EDT 2019. Contains 325168 sequences. (Running on oeis4.)