%I #4 Oct 28 2012 12:56:57
%S 60,292,292,1176,2396,1176,4272,15584,15584,4272,14580,88178,156120,
%T 88178,14580,47804,455108,1310228,1310228,455108,47804
%N Coefficients of the Pascal sequence minus the Eulerian numbers with first and last columns subtracted: f(n)=2^n - 2n; q(x,n)= = (1 - x)^(n + 1)*PolyLog[ -n, x]; p(x,n) = ((q(x, n)/x - (x + 1)^(n - 1))/x - f[n] - f[n]*x^(n - 3))/x.
%C Row sums are:{60, 584, 4748, 39712, 361636, 3626280}. First row elements/column are: {60, 292, 1176, 4272, 14580, 47804}.
%F f(n)=2^n - 2n; q(x,n)= = (1 - x)^(n + 1)*PolyLog[ -n, x]; p(x,n) = ((q(x, n)/x - (x + 1)^(n - 1))/x - f[n] - f[n]*x^(n - 3))/x; t(n,m)=Coefficients(p(x,n)).
%e {2}, {8, 8}, {22, 60, 22}, {52, 292, 292, 52}, {114, 1176, 2396, 1176, 114}, {240, 4272, 15584, 15584, 4272, 240}, {494, 14580, 88178, 156120, 88178, 14580, 494}, {1004, 47804, 455108, 1310228, 1310228, 455108, 47804, 1004}
%t f[n_] = 2^n - 2n; q[x_, n_] = (1 - x)^(n + 1)*PolyLog[ -n, x]; p[x_, n_] = ((q[x, n]/x - (x + 1)^(n - 1))/x - f[n] - f[n]*x^(n - 3))/x Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 5, 10}] Flatten[%]
%Y A005803
%K nonn
%O 5,1
%A _Roger L. Bagula_, Nov 01 2008