A146749 - OEIS

%I #5 Nov 03 2022 10:15:11

%S 2,8,8,22,60,22,52,292,292,52,114,1176,2396,1176,114,240,4272,15584,

%T 15584,4272,240,494,14580,88178,156120,88178,14580,494,1004,47804,

%U 455108,1310228,1310228,455108,47804,1004

%N Coefficients of the Pascal sequence minus the Eulerian numbers: q(x,n)= = (1 - x)^(n + 1)*PolyLog[ -n, x]; p(x,n) = (q(x, n)/x - (x + 1)^(n - 1))/x.

%C Row sums are: {2, 16, 104, 688, 4976, 40192, 362624, 3628288}.

%C First row elements/column are A005803;f(n)=2^n - 2n; {2, 8, 22, 52, 114, 240, 494, 1004}.

%F q(x,n) = (1 - x)^(n + 1)*PolyLog[ -n, x]; p(x,n) = (q(x, n)/x - (x + 1)^(n - 1))/x; t(n,m)=Coefficients(p(x,n)).

%e Triangle begins:

%e   {2},

%e   {8, 8},

%e   {22, 60, 22},

%e   {52, 292, 292, 52},

%e   {114, 1176, 2396, 1176, 114},

%e   {240, 4272, 15584, 15584, 4272, 240},

%e   {494, 14580, 88178, 156120, 88178, 14580, 494},

%e   {1004, 47804, 455108, 1310228, 1310228, 455108, 47804, 1004}

%e   ...

%t q[x_, n_] = (1 - x)^(n + 1)*PolyLog[ -n, x]; p[x_, n_] = (q[x, n]/x - (x + 1)^(n - 1))/x; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 3, 10}]; Flatten[%]

%Y Cf. A005803.

%K nonn,tabf

%O 3,1

%A _Roger L. Bagula_, Nov 01 2008