A156046 A triangle sequence made symmetrical by reverse coefficients: t0(n,m)=(2 + n! - m! - (n - m)! + 2 + PartitionsP[n] - PartitionsP[ m] - PartitionsP[n - m]); t(n,m)=(t0(n,m)+Reverse[t0(n,m)])/2

2, 2, 2, 2, 4, 2, 2, 7, 7, 2, 2, 22, 25, 22, 2, 2, 100, 118, 118, 100, 2, 2, 606, 702, 717, 702, 606, 2, 2, 4326, 4928, 5021, 5021, 4928, 4326, 2, 2, 35289, 39611, 40210, 40288, 40210, 39611, 35289, 2, 2, 322570, 357855, 362174, 362758, 362758, 362174, 357855

Offset

0,1

Comments

Row sums are:

{2, 4, 8, 18, 73, 440, 3337, 28554, 270512, 2810718, 31841200,...}.

When divided by two this sequence is very close to Pascal's triangle,

Links

Table of n, a(n) for n=0..52.

Formula

t0(n,m)=(2 + n! - m! - (n - m)! + 2 + PartitionsP[n] - PartitionsP[ m] - PartitionsP[n - m]);

t(n,m)=(t0(n,m)+Reverse[t0(n,m)])/2

Example

{2},
{2, 2},
{2, 4, 2},
{2, 7, 7, 2},
{2, 22, 25, 22, 2},
{2, 100, 118, 118, 100, 2},
{2, 606, 702, 717, 702, 606, 2},
{2, 4326, 4928, 5021, 5021, 4928, 4326, 2},
{2, 35289, 39611, 40210, 40288, 40210, 39611, 35289, 2},
{2, 322570, 357855, 362174, 362758, 362758, 362174, 357855, 322570, 2},
{2, 3265934, 3588500, 3623782, 3628086, 3628592, 3628086, 3623782, 3588500, 3265934, 2}

Mathematica

Clear[t];
t[n_, m_] =(2 + n! - m! - (n - m)! + 2 + PartitionsP[n] - PartitionsP[ m] - PartitionsP[n - m]);
Table[(Table[t[n, m], {m, 0, n}] + Reverse[Table[t[n, m], {m, 0, n}]])/2, {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A250200 A097859 A028326 * A048003 A098219 A368883

Adjacent sequences: A156043 A156044 A156045 * A156047 A156048 A156049

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Feb 02 2009

Status

approved