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]

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

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