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A174730 A symmetrical triangle sequence:q=4:t(n,m,q)=(1 - q^n)*Eulerian[n + 1, m] - (1 - q^n) + 1 0
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 (list; table; graph; refs; listen; history; text; internal format)
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: A271141 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

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Last modified January 27 04:57 EST 2020. Contains 331291 sequences. (Running on oeis4.)