A146749 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.

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

Offset

3,1

Comments

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

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

Links

Table of n, a(n) for n=3..38.

Formula

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)).

Example

Triangle begins:
  {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}
  ...

Mathematica

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[%]

Crossrefs

Cf. A005803.

Sequence in context: A093907 A116471 A364294 * A250313 A180825 A230708

Adjacent sequences: A146746 A146747 A146748 * A146750 A146751 A146752

Keyword

nonn,tabf

Author

Roger L. Bagula, Nov 01 2008

Status

approved