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%I #2 Mar 30 2012 17:34:40
%S 1,0,-1,4,-3,1,64,-36,9,-1,1296,-650,147,-18,1,32768,-15440,3330,-415,
%T 30,-1,1000000,-452984,95070,-11915,945,-45,1,35831808,-15796032,
%U 3257240,-409290,33985,-1869,63,-1,1475789056,-637771728,129899980
%N A triangle sequence from coefficients of an infinite sum polynomial: p(x,n)=Sum[(n - k - 1)^n*Binomial[x, k], {k, 0, Infinity}]/2^(x - n)
%C Row sums are:
%C {1, -1, 2, 36, 776, 20272, 631072, 22915904, 952885376, 44690261760,
%C 2334989427200,...}.
%F p(x,n)=Sum[(n - k - 1)^n*Binomial[x, k], {k, 0, Infinity}]/2^(x - n);
%F t(n,m)=coefficients(p(x,n))
%e {1},
%e {0, -1},
%e {4, -3, 1},
%e {64, -36, 9, -1},
%e {1296, -650, 147, -18, 1},
%e {32768, -15440, 3330, -415, 30, -1},
%e {1000000, -452984, 95070, -11915, 945, -45, 1},
%e {35831808, -15796032, 3257240, -409290, 33985, -1869, 63, -1},
%e {1475789056, -637771728, 129899980, -16347156, 1394785, -82824, 3346, -84, 1},
%e {68719476736, -29249804544, 5903488080, -743652588, 64602132, -4022361, 179760, -5562, 108, -1},
%e {3570467226624, -1501631050304, 300957690720, -37937816820, 3338126820, -214628631, 10227105, -356910, 8730, -135, 1}
%t p[x_, n_] := Sum[(n - k - 1)^n*Binomial[x, k], {k, 0, Infinity}]/2^(x - n);
%t Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];
%t Flatten[%]
%K sign,tabl,uned
%O 0,4
%A _Roger L. Bagula_, Apr 27 2010
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