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A174387 A symmetrical product triangle sequence:q=2;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)] 1
1, 1, 1, 1, -3, 1, 1, -7, -7, 1, 1, -15, 105, -15, 1, 1, -31, 465, 465, -31, 1, 1, -63, 1953, -29295, 1953, -63, 1, 1, -127, 8001, -248031, -248031, 8001, -127, 1, 1, -255, 32385, -2040255, 63247905, -2040255, 32385, -255, 1, 1, -511, 130305, -16548735 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, -1, -12, 77, 870, -25513, -480312, 59231657, 2052302730,

-1032956270773,...}.

LINKS

Table of n, a(n) for n=0..48.

FORMULA

q=2;

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, -3, 1},

{1, -7, -7, 1},

{1, -15, 105, -15, 1},

{1, -31, 465, 465, -31, 1},

{1, -63, 1953, -29295, 1953, -63, 1},

{1, -127, 8001, -248031, -248031, 8001, -127, 1},

{1, -255, 32385, -2040255, 63247905, -2040255, 32385, -255, 1},

{1, -511, 130305, -16548735, 1042570305, 1042570305, -16548735, 130305, -511, 1},

{1, -1023, 522753, -133302015, 16929355905, -1066549422015, 16929355905, -133302015, 522753, -1023, 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: A058669 A057004 A059328 * A176791 A259471 A220555

Adjacent sequences:  A174384 A174385 A174386 * A174388 A174389 A174390

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Mar 18 2010

STATUS

approved

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Last modified July 18 19:00 EDT 2019. Contains 325144 sequences. (Running on oeis4.)