A174730 A symmetrical triangle sequence:q=4:t(n,m,q)=(1 - q^n)*Eulerian[n + 1, m] - (1 - q^n) + 1.

1, 1, 1, 1, -44, 1, 1, -629, -629, 1, 1, -6374, -16574, -6374, 1, 1, -57287, -307922, -307922, -57287, 1, 1, -487304, -4873049, -9889424, -4873049, -487304, 1, 1, -4030217, -70315835, -255869693, -255869693, -70315835, -4030217, 1, 1

Offset

0,5

Comments

Row sums are:

{1, 2, -42, -1256, -29320, -730416, -20610128, -660431488, -23780750976,

-951261896960, -41855747025664,...}.

Links

Table of n, a(n) for n=0..36.

Formula

q=4:t(n,m,q)=(1 - q^n)*Eulerian[n + 1, m] - (1 - q^n) + 1.

Example

{1},
{1, 1},
{1, -44, 1},
{1, -629, -629, 1},
{1, -6374, -16574, -6374, 1},
{1, -57287, -307922, -307922, -57287, 1},
{1, -487304, -4873049, -9889424, -4873049, -487304, 1},
{1, -4030217, -70315835, -255869693, -255869693, -70315835, -4030217, 1},
{1, -32833034, -957269744, -5782349654, -10235846114, -5782349654, -957269744, -32833034, 1},
{1, -265288715, -12540658976, -119325134312, -343499866478, -343499866478, -119325134312, -12540658976, -265288715, 1},
{1, -2133850124, -160050293699, -2310521381024, -10211141838974, -16488052298024, -10211141838974, -2310521381024, -160050293699, -2133850124, 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: A350718 A022075 A178986 * A037939 A040010 A169857

Adjacent sequences: A174727 A174728 A174729 * A174731 A174732 A174733

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Mar 28 2010

Status

approved