A174729 A symmetrical triangle sequence:q=3:t(n,m,q)=(1 - q^n)*Eulerian[n + 1, m] - (1 - q^n) + 1

1, 1, 1, 1, -23, 1, 1, -259, -259, 1, 1, -1999, -5199, -1999, 1, 1, -13551, -72841, -72841, -13551, 1, 1, -86631, -866319, -1758119, -866319, -86631, 1, 1, -537755, -9382311, -34140947, -34140947, -9382311, -537755, 1, 1, -3286559, -95821919

Offset

0,5

Comments

Row sums are:

{1, 2, -21, -516, -9195, -172782, -3664017, -88122024, -2380433751,

-71421844770, -2357006556861,...}.

Links

Table of n, a(n) for n=0..38.

Formula

q=3:t(n,m,q)=(1 - q^n)*Eulerian[n + 1, m] - (1 - q^n) + 1

Example

{1},
{1, 1},
{1, -23, 1},
{1, -259, -259, 1},
{1, -1999, -5199, -1999, 1},
{1, -13551, -72841, -72841, -13551, 1},
{1, -86631, -866319, -1758119, -866319, -86631, 1},
{1, -537755, -9382311, -34140947, -34140947, -9382311, -537755, 1},
{1, -3286559, -95821919, -578808479, -1024599839, -578808479, -95821919, -3286559, 1},
{1, -19918183, -941567197, -8959069261, -25790367745, -25790367745, -8959069261, -941567197, -19918183, 1},
{1, -120162679, -9012850527, -130111500375, -575016096423, -928485336855, -575016096423, -130111500375, -9012850527, -120162679, 1}

Mathematica

<< DiscreteMath`Combinatorica`
t[n_, m_, q_] = (1 - q^n)*Eulerian[n + 1, m] - (1 - q^n) + 1;
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]

Crossrefs

Sequence in context: A040529 A234788 A144445 * A022186 A015151 A040539

Adjacent sequences: A174726 A174727 A174728 * A174730 A174731 A174732

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Mar 28 2010

Status

approved