A176390 A symmetrical triangle:t(n,m)=1 - (1 + n)^(n + 1)* (1 - 1/(n + 1))^(n + 1) + (n + 1)^(n + 2)*Binomial[n, m]((m + 1)/(n + 1))^(m + 1)*(1 - ( m + 1)/(n + 1))^(n - m + 1)

1, 1, 1, 1, 16, 1, 1, 273, 273, 1, 1, 4856, 6246, 4856, 1, 1, 95065, 134785, 134785, 95065, 1, 1, 2073408, 3094575, 3410240, 3094575, 2073408, 1, 1, 50255905, 77413889, 89782273, 89782273, 77413889, 50255905, 1, 1, 1345053808, 2116602172

Offset

0,5

Comments

The sequence is an adjusted probability based symmetrical triangle.

Row sums are:

{1, 2, 18, 548, 15960, 459702, 13746208, 434904136, 14654790000, 526697204570,...}.

Links

Table of n, a(n) for n=0..38.

Formula

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

Example

{1},
{1, 1},
{1, 16, 1},
{1, 273, 273, 1},
{1, 4856, 6246, 4856, 1},
{1, 95065, 134785, 134785, 95065, 1},
{1, 2073408, 3094575, 3410240, 3094575, 2073408, 1},
{1, 50255905, 77413889, 89782273, 89782273, 77413889, 50255905, 1},
{1, 1345053808, 2116602172, 2532959344, 2665559350, 2532959344, 2116602172, 1345053808, 1},
{1, 39471376041, 63074539521, 77094686721, 83708000001, 83708000001, 77094686721, 63074539521, 39471376041, 1}

Mathematica

t[n_, m_] = 1 - (1 + n)^(n + 1)* (1 - 1/(n + 1))^(n + 1) + (n + 1)^(n + 2)*Binomial[n, m]((m + 1)/(n + 1))^(m + 1)*(1 - (m + 1)/(n + 1))^(n - m + 1);
Table[Table[t[n, m], {m, 0, n - 1}], {n, 1, 10}];
Flatten[%]

Crossrefs

Sequence in context: A173585 A022179 A015141 * A178062 A040263 A082696

Adjacent sequences: A176387 A176388 A176389 * A176391 A176392 A176393

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 16 2010

Status

approved