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A174921 A symmetrical triangle sequence:q=4;c(n,q)=Product[(1 - q^i), {i, 1, n}]:t(n,m)=1 + Binomial[n, m]^2 + (c(n, q)/(c(m, q)*c(n - m, q)))^2 - 2*Binomial[n, m]*c(n, q)/(c(m, q)*c(n - m, q)) 0
1, 1, 1, 1, 10, 1, 1, 325, 325, 1, 1, 6562, 123202, 6562, 1, 1, 112897, 33489370, 33489370, 112897, 1, 1, 1846882, 8663514085, 141966936226, 8663514085, 1846882, 1, 1, 29746117, 2222580052225, 586055248782085, 586055248782085 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 12, 652, 136328, 67204536, 159297658162, 1176555717160856,

43519834692800379792, 5103194797279049583074896,

3003810774554741345908169533490,...}.

LINKS

Table of n, a(n) for n=0..32.

FORMULA

q=4;

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

t(n,m)=1 + Binomial[n, m]^2 + (c(n, q)/(c(m, q)*c(n - m, q)))^2 - 2*Binomial[n, m]*c(n, q)/(c(m, q)*c(n - m, q))

EXAMPLE

{1},

{1, 1},

{1, 10, 1},

{1, 325, 325, 1},

{1, 6562, 123202, 6562, 1},

{1, 112897, 33489370, 33489370, 112897, 1},

{1, 1846882, 8663514085, 141966936226, 8663514085, 1846882, 1},

{1, 29746117, 2222580052225, 586055248782085, 586055248782085, 2222580052225, 29746117, 1},

{1, 476854570, 569255746164562, 2405110998912836842, 38708474182528667842, 2405110998912836842, 569255746164562, 476854570, 1},

{1, 7633866385, 145746464523607810, 9856072134501813576226, 2541741180758550820487026, 2541741180758550820487026, 9856072134501813576226, 145746464523607810, 7633866385, 1},

{1, 122160735226, 37312168908143937601, 40375323007070415995666026, 166656597689187698199553355626, 2670416828455727470616462144530, 166656597689187698199553355626, 40375323007070415995666026, 37312168908143937601, 122160735226, 1}

MATHEMATICA

Clear[t, n, m, c, q]

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

t[n_, m_, q_] = 1 + Binomial[n, m]^2 + (c[n, q]/(c[m, q]*c[n - m, q]))^2 - 2*Binomial[n, m]*c[n, q]/(c[m, q]*c[n - m, q])

Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]

CROSSREFS

Sequence in context: A172378 A015124 A156767 * A010180 A109013 A213790

Adjacent sequences:  A174918 A174919 A174920 * A174922 A174923 A174924

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Apr 02 2010

STATUS

approved

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Last modified January 23 19:12 EST 2020. Contains 331175 sequences. (Running on oeis4.)