A176565 A symmetrical triangle:t(n,m)=Binomial[PartitionsP[n] + m, m] + Binomial[PartitionsP[n] + n - m, n - m] - (Binomial[PartitionsP[n] + 0, 0] + Binomial[PartitionsP[ n] + n - 0, n - 0]) + 1

1, 1, 1, 1, 0, 1, 1, -6, -6, 1, 1, -64, -84, -64, 1, 1, -454, -636, -636, -454, 1, 1, -7996, -10933, -11648, -10933, -7996, 1, 1, -116264, -154904, -165852, -165852, -154904, -116264, 1, 1, -4292122, -5475909, -5769895, -5823025, -5769895, -5475909

Offset

0,8

Comments

Row sums are:

{1, 2, 2, -10, -210, -2178, -49504, -874038, -36898875, -1572273560,

-135022067180,...}.

Links

Table of n, a(n) for n=0..42.

Formula

t(n,m)=Binomial[PartitionsP[n] + m, m] + Binomial[PartitionsP[n] + n - m, n - m] - (Binomial[PartitionsP[n] + 0, 0] + Binomial[PartitionsP[ n] + n - 0, n - 0]) + 1

Example

{1},
{1, 1},
{1, 0, 1},
{1, -6, -6, 1},
{1, -64, -84, -64, 1},
{ 1, -454, -636, -636, -454, 1},
{1, -7996, -10933, -11648, -10933, -7996, 1},
{1, -116264, -154904, -165852, -165852, -154904, -116264, 1},
{1, -4292122, -5475909, -5769895, -5823025, -5769895, -5475909, -4292122, 1},
{1, -163011609, -201619164, -209961884, -211544124, -211544124, -209961884, -201619164, -163011609, 1},
{1, -12777711827, -15283144624, -15734109446, -15807589523, -15816956342, -15807589523, -15734109446, -15283144624, -12777711827, 1}

Mathematica

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

Crossrefs

Sequence in context: A205457 A155868 A322622 * A176567 A283100 A065493

Adjacent sequences: A176562 A176563 A176564 * A176566 A176567 A176568

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Apr 20 2010

Status

approved