A176417 A symmetrical triangle sequence;q=2;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, 2, 1, 1, 9, 9, 1, 1, 67, 117, 67, 1, 1, 625, 1741, 1741, 625, 1, 1, 6841, 30529, 49501, 30529, 6841, 1, 1, 86401, 635041, 1695745, 1695745, 635041, 86401, 1, 1, 1244881, 15504481, 69911281, 115612993, 69911281, 15504481, 1244881, 1, 1

Offset

0,5

Comments

Row sums are:

{1, 2, 4, 20, 253, 4734, 124243, 4834376, 288934281, 26786718730,

3842906762891,...}.

Links

Table of n, a(n) for n=0..45.

Formula

q=2;

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, 2, 1},
{1, 9, 9, 1},
{1, 67, 117, 67, 1},
{1, 625, 1741, 1741, 625, 1},
{1, 6841, 30529, 49501, 30529, 6841, 1},
{1, 86401, 635041, 1695745, 1695745, 635041, 86401, 1},
{1, 1244881, 15504481, 69911281, 115612993, 69911281, 15504481, 1244881, 1},
{1, 20240641, 437461921, 3403948321, 9531708481, 9531708481, 3403948321, 437461921, 20240641, 1},
{1, 367597441, 14047971841, 191951272801, 928692466561, 1572788145601, 928692466561, 191951272801, 14047971841, 367597441, 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: A141601 A108558 A128434 * A119731 A368928 A283321

Adjacent sequences: A176414 A176415 A176416 * A176418 A176419 A176420

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 17 2010

Status

approved