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A176419 A symmetrical triangle sequence;q=4;c(n,q)=Product[1 - q^i, {i, 1, n}];t(n,m,q)=1 - n! + n!*c(n, q)/(c[m, q)*c(n - m, q))/Binomial[n, m] 0
1, 1, 1, 1, 4, 1, 1, 37, 37, 1, 1, 487, 1405, 487, 1, 1, 8065, 69445, 69445, 8065, 1, 1, 163081, 4467745, 13564261, 4467745, 163081, 1, 1, 3926881, 357799681, 3486035233, 3486035233, 357799681, 3926881, 1, 1, 110058481, 34357076641 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 6, 76, 2381, 155022, 22825915, 7695523592, 5885796151305,

10048538573544970, 38025550094216572811,...}.

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

EXAMPLE

{1},

{1, 1},

{1, 4, 1},

{1, 37, 37, 1},

{1, 487, 1405, 487, 1},

{1, 8065, 69445, 69445, 8065, 1},

{1, 163081, 4467745, 13564261, 4467745, 163081, 1},

{1, 3926881, 357799681, 3486035233, 3486035233, 357799681, 3926881, 1},

{1, 110058481, 34357076641, 1116606260881, 3583649359297, 1116606260881, 34357076641, 110058481, 1},

{1, 3522839041, 3848216934241, 428879890648801, 4591537656350401, 4591537656350401, 428879890648801, 3848216934241, 3522839041, 1},

{1, 126832003201, 492578856806401, 192149735821495201, 7054317360272016001, 23531630490651931201, 7054317360272016001, 192149735821495201, 492578856806401, 126832003201, 1}

MATHEMATICA

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

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

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

CROSSREFS

Sequence in context: A209196 A158390 A228836 * A299471 A102602 A156951

Adjacent sequences:  A176416 A176417 A176418 * A176420 A176421 A176422

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Apr 17 2010

STATUS

approved

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Last modified April 23 08:53 EDT 2021. Contains 343204 sequences. (Running on oeis4.)