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A176022 A symmetrical triangle sequence:t(n,m)= ((-1)^n* Binomial[ -1 + n, -1 + m] Binomial[ n, -1 + m] n!/(m*m!)) + ((-1)^n* Binomial[ -1 + n, -m + n] Binomial[n, -m + n] n!)/((1 - m + n) ( 1 - m + n)!) 0
-2, 3, 3, -7, -18, -7, 25, 96, 96, 25, -121, -650, -800, -650, -121, 721, 5490, 7500, 7500, 5490, 721, -5041, -53067, -92610, -73500, -92610, -53067, -5041, 40321, 564704, 1328096, 987840, 987840, 1328096, 564704, 40321, -362881, -6532164 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row sums are:

{-2, 6, -32, 242, -2342, 27422, -374936, 5841922, -101897354, 1962916022,...}.

LINKS

Table of n, a(n) for n=1..38.

FORMULA

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

EXAMPLE

{-2},

{3, 3},

{-7, -18, -7},

{25, 96, 96, 25},

{-121, -650, -800, -650, -121},

{721, 5490, 7500, 7500, 5490, 721},

{-5041, -53067, -92610, -73500, -92610, -53067, -5041},

{40321, 564704, 1328096, 987840, 987840, 1328096, 564704, 40321},

{-362881, -6532164, -20345472, -18373824, -10668672, -18373824, -20345472, -6532164, -362881},

{3628801, 81648450, 326640600, 382838400, 186701760, 186701760, 382838400, 326640600, 81648450, 3628801}

MATHEMATICA

L[n_, m_] = ((-1)^n* Binomial[ -1 + n, -1 + m] Binomial[ n, -1 + m] n!/(m*m!)) + ((-1)^n* Binomial[ -1 + n, -m + n] Binomial[n, -m + n] n!)/((1 - m + n) ( 1 - m + n)!);

Table[Table[L[n, m], {m, 1, n}], {n, 1, 10}];

Flatten[%]

CROSSREFS

Cf. A008297

Sequence in context: A136122 A121875 A036251 * A113031 A127582 A157144

Adjacent sequences:  A176019 A176020 A176021 * A176023 A176024 A176025

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Apr 06 2010

STATUS

approved

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Last modified May 26 07:30 EDT 2017. Contains 287093 sequences.