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A176094 A symmetrical triangle sequence:t(n,m)=Sum[(-1)^k*(n + m)!/(( n - k)!*(m - k)!*k!), {k, 0, m}] + Sum[(-1)^k*(n + (n - m))!/((n - k)!*((n - m) - k)!*k!), {k, 0, (n - m)}];t1(n,m)=t(n,m)-t(n,0)+1 0
1, 1, 1, 1, 0, 1, 1, -78, -78, 1, 1, 1070, 1200, 1070, 1, 1, -16530, -14665, -14665, -16530, 1, 1, 240667, 179242, 163044, 179242, 240667, 1, 1, -2572332, -726012, -638358, -638358, -726012, -2572332, 1, 1, -29453058, -82571646, -81432978 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Row sums are:

{1, 2, 2, -154, 3342, -62388, 1002864, -7873402, -466190602, 41337748316,

-2470134563444,...}.

LINKS

Table of n, a(n) for n=0..39.

FORMULA

t(n,m)=Sum[(-1)^k*(n + m)!/(( n - k)!*(m - k)!*k!), {k, 0, m}] + Sum[(-1)^k*(n + (n - m))!/((n - k)!*((n - m) - k)!*k!), {k, 0, (n - m)}];

;t1(n,m)=t(n,m)-t(n,0)+1

EXAMPLE

{1},

{1, 1},

{1, 0, 1},

{1, -78, -78, 1},

{1, 1070, 1200, 1070, 1},

{1, -16530, -14665, -14665, -16530, 1},

{1, 240667, 179242, 163044, 179242, 240667, 1},

{1, -2572332, -726012, -638358, -638358, -726012, -2572332, 1},

{1, -29453058, -82571646, -81432978, -79275240, -81432978, -82571646, -29453058, 1},

{1, 4090911030, 5625623025, 5495184255, 5457155847, 5457155847, 5495184255, 5625623025, 4090911030, 1},

{1, -244272466537, -288270741792, -281432018582, -280618259207, -280947591210, -280618259207, -281432018582, -288270741792, -244272466537, 1}

MATHEMATICA

t[n_, m_] = Sum[(-1)^k*(n + m)!/(( n - k)!*(m - k)!*k!), {k, 0, m}] + Sum[(-1)^k*(n + (n - m))!/((n - k)!*((n - m) - k)!*k!), {k, 0, (n - m)}];

Table[Table[t[n, m] - t[n, 0] + 1, {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A117330 A033398 A204376 * A124289 A181467 A217006

Adjacent sequences:  A176091 A176092 A176093 * A176095 A176096 A176097

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Apr 08 2010

STATUS

approved

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Last modified December 19 16:03 EST 2014. Contains 252236 sequences.