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A174389 A symmetrical product triangle sequence:q=4;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, -15, 1, 1, -63, -63, 1, 1, -255, 16065, -255, 1, 1, -1023, 260865, 260865, -1023, 1, 1, -4095, 4189185, -1068242175, 4189185, -4095, 1, 1, -16383, 67088385, -68631417855, -68631417855, 67088385, -16383, 1, 1, -65535, 1073659905 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, -13, -124, 15557, 519686, -1059871993, -137128691704, 4488968841694217,

2304532518723444746, -1207942486943791238467573,...}.

LINKS

Table of n, a(n) for n=0..38.

FORMULA

q=4;

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, -15, 1},

{1, -63, -63, 1},

{1, -255, 16065, -255, 1},

{1, -1023, 260865, 260865, -1023, 1},

{1, -4095, 4189185, -1068242175, 4189185, -4095, 1},

{1, -16383, 67088385, -68631417855, -68631417855, 67088385, -16383, 1},

{1, -65535, 1073659905, -4396637310975, 4497759969127425, -4396637310975, 1073659905, -65535, 1},

{1, -262143, 17179541505, -281452428476415, 1152547694610919425, 1152547694610919425, -281452428476415, 17179541505, -262143, 1},

{1, -1048575, 274876596225, -18014037733605375, 295123980189656858625, -1208532698876644836069375, 295123980189656858625, -18014037733605375, 274876596225, -1048575, 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: A172429 A040225 A070644 * A176286 A111805 A238754

Adjacent sequences:  A174386 A174387 A174388 * A174390 A174391 A174392

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Mar 18 2010

STATUS

approved

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Last modified October 20 07:33 EDT 2019. Contains 328252 sequences. (Running on oeis4.)