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A176647 A symmetrical triangle sequence:t(n,m)=Binomial[n*(3*n - 1)/2 + m, m] + Binomial[n*(3*n - 1)/2 + n - m, n - m] - Binomial[n + n*(3*n - 1)/2, n] 0
1, 1, 1, 1, -9, 1, 1, -351, -351, 1, 1, -12627, -14398, -12627, 1, 1, -575721, -648906, -648906, -575721, 1, 1, -32468384, -35945819, -36238644, -35945819, -32468384, 1, 1, -2186189329, -2387546394, -2403595518, -2403595518, -2387546394 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The sequence uses pentagonal numbers as the connectedness function.

Row sums are:

{1, 2, -7, -700, -39650, -2449252, -173067048, -13954662480, -1270600138500,

-129219696586750, -14534235944709635,...}.

LINKS

Table of n, a(n) for n=0..33.

FORMULA

t(n,m)=Binomial[n*(3*n - 1)/2 + m, m] + Binomial[n*(3*n - 1)/2 + n - m, n - m] - Binomial[n + n*(3*n - 1)/2, n]

EXAMPLE

{1},

{1, 1},

{1, -9, 1},

{1, -351, -351, 1},

{1, -12627, -14398, -12627, 1},

{1, -575721, -648906, -648906, -575721, 1},

{1, -32468384, -35945819, -36238644, -35945819, -32468384, 1},

{1, -2186189329, -2387546394, -2403595518, -2403595518, -2387546394, -2186189329, 1},

{1, -171200862663, -185035271537, -186023309861, -186081250380, -186023309861, -185035271537, -171200862663, 1},

{1, -15290266473507, -16391165652705, -16462191132828, -16466225034336, -16466225034336, -16462191132828, -16391165652705, -15290266473507, 1},

{1, -1534076755992789, -1633692129747979, -1639551857097889, -1639860244637209, -1639873969757905, -1639860244637209, -1639551857097889, -1633692129747979, -1534076755992789, 1}

MATHEMATICA

t[n_, m_] = Binomial[n*( 3*n - 1)/2 + m, m] + Binomial[n*(3*n - 1)/2 + n - m, n - m] - Binomial[n + n*(3*n - 1)/2, n];

Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Cf. A000326, A176567

Sequence in context: A022172 A173005 A015123 * A068452 A021527 A257437

Adjacent sequences:  A176644 A176645 A176646 * A176648 A176649 A176650

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Apr 22 2010

STATUS

approved

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Last modified April 19 10:30 EDT 2021. Contains 343112 sequences. (Running on oeis4.)