A146750 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.

60, 292, 292, 1176, 2396, 1176, 4272, 15584, 15584, 4272, 14580, 88178, 156120, 88178, 14580, 47804, 455108, 1310228, 1310228, 455108, 47804

Offset

5,1

Comments

Row sums are:{60, 584, 4748, 39712, 361636, 3626280}. First row elements/column are: {60, 292, 1176, 4272, 14580, 47804}.

Links

Table of n, a(n) for n=5..25.

Formula

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)).

Example

{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

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[%]

Crossrefs

A005803

Sequence in context: A338109 A179811 A268805 * A298045 A063497 A096363

Adjacent sequences: A146747 A146748 A146749 * A146751 A146752 A146753

Keyword

nonn

Author

Roger L. Bagula, Nov 01 2008

Status

approved