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A174732 A symmetrical triangle sequence:q=3:t(n,m,q)=(1 - q^n)*(Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m) - (1 - q^n) + 1 0
1, 1, 1, 1, -51, 1, 1, -399, -399, 1, 1, -2177, -4597, -2177, 1, 1, -10191, -35671, -35671, -10191, 1, 1, -43719, -227343, -380363, -227343, -43719, 1, 1, -177119, -1279199, -3207839, -3207839, -1279199, -177119, 1, 1, -688869, -6593469 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, -49, -796, -8949, -91722, -922485, -9328312, -95516737, -991179718,...}.

LINKS

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

FORMULA

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

EXAMPLE

{1},

{1, 1},

{1, -51, 1},

{1, -399, -399, 1},

{1, -2177, -4597, -2177, 1},

{1, -10191, -35671, -35671, -10191, 1},

{1, -43719, -227343, -380363, -227343, -43719, 1},

{1, -177119, -1279199, -3207839, -3207839, -1279199, -177119, 1}, {1, -688869, -6593469, -23126349, -34699365, -23126349, -6593469, -688869, 1},

{1, -2598111, -31826871, -148741911, -312422967, -312422967, -148741911, -31826871, -2598111, 1}

MATHEMATICA

<< DiscreteMath`Combinatorica`

t[n_, m_, q_] = =(1 - q^n)*(Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m) - (1 - q^n) + 1;

Table[Flatten[Table[Table[t[n, m, q], {m, 1, n}], {n, 1, 10}]], {q, 2, 12}]

CROSSREFS

Sequence in context: A015038 A152515 A111402 * A087408 A255852 A160474

Adjacent sequences:  A174729 A174730 A174731 * A174733 A174734 A174735

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Mar 28 2010

STATUS

approved

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Last modified February 25 11:39 EST 2020. Contains 332233 sequences. (Running on oeis4.)