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A169654 A symmetrical triangle sequence:t(n,m)=A008297(n,m)+A008297(n,n-m+1)-(A008297(n,1)+A008297(n,n))+1 0
1, 1, 1, 1, -4, 1, 1, 24, 24, 1, 1, -138, -118, -138, 1, 1, 1110, 780, 780, 1110, 1, 1, -10120, -8188, -3358, -8188, -10120, 1, 1, 100856, 101976, 30240, 30240, 101976, 100856, 1, 1, -1088710, -1332574, -512062, -60478, -512062, -1332574, -1088710 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are:

{1, 2, -2, 50, -392, 3782, -39972, 466146, -5927168, 81594182,...}.

LINKS

Table of n, a(n) for n=1..44.

FORMULA

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

t(n,m)=L(n, m) + L(n, n - m + 1)-(L(n, 1) + L(n, n ))+1

EXAMPLE

{1},

{1, 1},

{1, -4, 1},

{1, 24, 24, 1},

{1, -138, -118, -138, 1},

{1, 1110, 780, 780, 1110, 1},

{1, -10120, -8188, -3358, -8188, -10120, 1},

{1, 100856, 101976, 30240, 30240, 101976, 100856, 1},

{1, -1088710, -1332574, -512062, -60478, -512062, -1332574, -1088710, 1},

{1, 12700890, 18147240, 9132480, 816480, 816480, 9132480, 18147240, 12700890, 1}

MATHEMATICA

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

t[n_, m_] = L[n, m] + L[n, n - m + 1];

Table[Table[t[n, m] - t[n, 1] + 1, {m, 1, n}], {n, 1, 10}];

Flatten[%]

CROSSREFS

Cf. A008297

Sequence in context: A016519 A113716 A220652 * A088158 A136449 A209427

Adjacent sequences:  A169651 A169652 A169653 * A169655 A169656 A169657

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Apr 05 2010

STATUS

approved

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Last modified January 28 00:32 EST 2020. Contains 331313 sequences. (Running on oeis4.)