A176418 A symmetrical triangle sequence;q=3;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, 3, 1, 1, 21, 21, 1, 1, 217, 497, 217, 1, 1, 2785, 14401, 14401, 2785, 1, 1, 42961, 527809, 1218961, 527809, 42961, 1, 1, 781921, 23866081, 133305985, 133305985, 23866081, 781921, 1, 1, 16490881, 1290574081, 18068561281

Offset

0,5

Comments

Row sums are:

{1, 2, 5, 44, 933, 34374, 2360503, 315907976, 82477228041, 41588066488330,

40120217923357451,...}.

Links

Table of n, a(n) for n=0..39.

Formula

q=3;

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, 3, 1},
{1, 21, 21, 1},
{1, 217, 497, 217, 1},
{1, 2785, 14401, 14401, 2785, 1},
{1, 42961, 527809, 1218961, 527809, 42961, 1},
{1, 781921, 23866081, 133305985, 133305985, 23866081, 781921, 1},
{1, 16490881, 1290574081, 18068561281, 43725975553, 18068561281, 1290574081, 16490881, 1},
{1, 396426241, 81341406721, 2930984939521, 17781310471681, 17781310471681, 2930984939521, 81341406721, 396426241, 1},
{1, 10710040321, 5857397360641, 554200243833601, 8653441003176961, 21693199214534401, 8653441003176961, 554200243833601, 5857397360641, 10710040321, 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: A016561 A111382 A173884 * A156950 A083998 A277170

Adjacent sequences: A176415 A176416 A176417 * A176419 A176420 A176421

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 17 2010

Status

approved