A176469 A symmetrical triangle:q=4;c(n,q)=Product[1 - q^i, {i, 1, n}];t(n,m,q)=A060187(n,m)-c(n,q)/(c(m,q)*c(n-m,q))+1.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, -8, -126, -8, 1, 1, -103, -4114, -4114, -103, 1, 1, -642, -82549, -353256, -82549, -642, 1, 1, -3281, -1430195, -23948889, -23948889, -1430195, -3281, 1, 1, -15292, -23527496, -1548356796, -6216938526

Offset: 0

Author

Roger L. Bagula, Apr 18 2010

Keywords

• sign
• tabl
• uned

Comments

Row sums are:

{1, 2, 4, 8, -140, -8432, -519636, -50764728, -9360737692, -3387701237632,

-246332974040099,...}.

Examples

			{1},
{1, 1},
{1, 2, 1},
{1, 3, 3, 1},
{1, -8, -126, -8, 1},
{1, -103, -4114, -4114, -103, 1},
{1, -642, -82549, -353256, -82549, -642, 1},
{ 1, -3281, -1430195, -23948889, -23948889, -1430195, -3281, 1},
{1, -15292, -23527496, -1548356796, -6216938526, -1548356796, -23527496, -15292, 1},
{1, -67707, -380011248, -99256044576, -1594214495286, -1594214495286, -99256044576, -380011248, -67707, 1},
{1, -290486, -6099252663, -6353979629820, -408235051426002, -1634139479203056, -408235051426002, -6353979629820, -6099252663, -290486, 1}
		

Crossrefs

Cf. A060187

Programs

Mathematica

(*A060187*);
p[x_, n_] = (1 - x)^(n + 1)*Sum[(2*k + 1)^n*x^k, {k, 0, Infinity}];
f[n_, m_] := CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x][[m + 1]];
c[n_, q_] = Product[1 - q^i, {i, 1, n}];
t[n_, m_, q_] := f[n, m] - c[n, q]/(c[m, q]*c[n - m, q]) + 1;
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]

Formula

q=4;

c(n,q)=Product[1 - q^i, {i, 1, n}];

t(n,m,q)=A060187(n,m)-c(n,q)/(c(m,q)*c(n-m,q))+1