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A174388 A symmetrical product triangle sequence:q=3;c(n,q)=Product[1 - q^i, {i, 1, n}]; t(n,m,q)=If[Floor[n/2] greater than or equal to m, c(n, q)/c(n - m, q), c(n, q)/c(m, q)] 0
1, 1, 1, 1, -8, 1, 1, -26, -26, 1, 1, -80, 2080, -80, 1, 1, -242, 19360, 19360, -242, 1, 1, -728, 176176, -14094080, 176176, -728, 1, 1, -2186, 1591408, -385120736, -385120736, 1591408, -2186, 1, 1, -6560, 14340160, -10439636480, 2526392028160 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, -6, -50, 1922, 38238, -13743182, -767063026, 2505541422402, 410381622528958,

-12099448759918102702,...}.

LINKS

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

FORMULA

q=3;

c(n,q)=Product[1 - q^i, {i, 1, n}];

t(n,m,q)=If[Floor[n/2] greater than or equal to m, c(n, q)/c(n - m, q), c(n, q)/c(m, q)]

EXAMPLE

{1},

{1, 1},

{1, -8, 1},

{1, -26, -26, 1},

{1, -80, 2080, -80, 1},

{1, -242, 19360, 19360, -242, 1},

{1, -728, 176176, -14094080, 176176, -728, 1},

{1, -2186, 1591408, -385120736, -385120736, 1591408, -2186, 1},

{1, -6560, 14340160, -10439636480, 2526392028160, -10439636480, 14340160, -6560, 1},

{1, -19682, 129113920, -282243029120, 205472925199360, 205472925199360, -282243029120, 129113920, -19682, 1},

{1, -59048, 1162182736, -7623918748160, 16665886383477760, -12132765287171809280, 16665886383477760, -7623918748160, 1162182736, -59048, 1}

MATHEMATICA

c[n_, q_] = Product[1 - q^i, {i, 1, n}];

t[n_, m_, q_] = If[Floor[n/2] >= m, c[n, q]/c[n - m, q], c[n, q]/c[m, q]];

Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 10}]

CROSSREFS

Sequence in context: A167034 A155452 A147295 * A220718 A176283 A323324

Adjacent sequences:  A174385 A174386 A174387 * A174389 A174390 A174391

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Mar 18 2010

STATUS

approved

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Last modified October 27 09:08 EDT 2020. Contains 338035 sequences. (Running on oeis4.)