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A176567 A symmetrical triangle sequence:t(n,m)=Binomial[Binomial[n, 2] + m, m] + Binomial[Binomial[n, 2] + n - m, n - m] - Binomial[n + Binomial[n, 2], n] 1
1, 1, 1, 1, 1, 1, 1, -6, -6, 1, 1, -119, -154, -119, 1, 1, -1991, -2651, -2651, -1991, 1, 1, -38744, -50252, -52632, -50252, -38744, 1, 1, -888008, -1118007, -1169366, -1169366, -1118007, -888008, 1, 1, -23535791, -28915001, -30018509, -30188420 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Row sums are:

{1, 2, 3, -10, -390, -9282, -230622, -6350760, -195127020, -6658198690,

-250521040770,...}.

Connectedness function is:

Binomial[n,2]=n*(n-1)/2

LINKS

Table of n, a(n) for n=0..40.

FORMULA

t(n,m)=Binomial[Binomial[n, 2] + m, m] + Binomial[Binomial[n, 2] + n - m, n - m] - Binomial[n + Binomial[n, 2], n]

EXAMPLE

{1},

{1, 1},

{1, 1, 1},

{1, -6, -6, 1},

{1, -119, -154, -119, 1},

{1, -1991, -2651, -2651, -1991, 1},

{1, -38744, -50252, -52632, -50252, -38744, 1},

{1, -888008, -1118007, -1169366, -1169366, -1118007, -888008, 1},

{1, -23535791, -28915001, -30018509, -30188420, -30018509, -28915001, -23535791, 1},

{1, -708930471, -853938318, -880908210, -885322347, -885322347, -880908210, -853938318, -708930471, 1},

{ 1, -23930713124, -28362325639, -29114847574, -29230428094, -29244411910, -29230428094, -29114847574, -28362325639, -23930713124, 1}

MATHEMATICA

t[n_, m_] = Binomial[ Binomial[n, 2] + m, m] + Binomial[Binomial[n, 2] + n - m, n - m] - Binomial[n + Binomial[n, 2], n];

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

Flatten[%]

CROSSREFS

Sequence in context: A155868 A322622 A176565 * A283100 A065493 A133890

Adjacent sequences:  A176564 A176565 A176566 * A176568 A176569 A176570

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Apr 22 2010

STATUS

approved

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Last modified May 8 08:39 EDT 2021. Contains 343666 sequences. (Running on oeis4.)