A176392 A symmetrical triangle:t(n,m)=2 - (1 + m)^m + (1 + n)^n - (1 - m + n)^(n - m)

1, 1, 1, 1, 7, 1, 1, 55, 55, 1, 1, 561, 609, 561, 1, 1, 7151, 7705, 7705, 7151, 1, 1, 109873, 117017, 117523, 117017, 109873, 1, 1, 1979503, 2089369, 2096465, 2096465, 2089369, 1979503, 1, 1, 40949569, 42929065, 43038883, 43045473, 43038883

Offset

0,5

Comments

Row sums are:

{1, 8, 111, 1732, 29713, 571304, 12330675, 296880508, 7909460021,

231346281432,...}.

Links

Table of n, a(n) for n=0..41.

Formula

t(n,m)=2 - (1 + m)^m + (1 + n)^n - (1 - m + n)^(n - m)

Example

{1},
{1, 1},
{1, 7, 1},
{1, 55, 55, 1},
{1, 561, 609, 561, 1},
{1, 7151, 7705, 7705, 7151, 1},
{1, 109873, 117017, 117523, 117017, 109873, 1},
{1, 1979503, 2089369, 2096465, 2096465, 2089369, 1979503, 1},
{1, 40949569, 42929065, 43038883, 43045473, 43038883, 42929065, 40949569, 1},
{1, 956953279, 997902841, 999882289, 999991601, 999991601, 999882289, 997902841, 956953279, 1},
{1, 24937424601, 25894377873, 25935327387, 25937306329, 25937409051, 25937306329, 25935327387, 25894377873, 24937424601, 1}

Mathematica

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

Crossrefs

Cf. A000169

Sequence in context: A174689 A172345 A174719 * A015118 A340428 A174691

Adjacent sequences: A176389 A176390 A176391 * A176393 A176394 A176395

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 16 2010

Status

approved