A176468 A symmetrical triangle:q=3;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, 3, 1, 1, 11, 11, 1, 1, 37, 101, 37, 1, 1, 117, 473, 473, 117, 1, 1, 359, -467, -10331, -467, 359, 1, 1, 1087, -38805, -666047, -666047, -38805, 1087, 1, 1, 3273, -564647, -22609991, -71238207, -22609991, -564647, 3273, 1, 1, 9833, -6313279

Offset: 0

Author

Roger L. Bagula, Apr 18 2010

Keywords

• sign
• tabl
• uned

Comments

Row sums are:

{1, 2, 5, 24, 177, 1182, -10545, -1407528, -117580935, -13535434518,

-2541110736213,...}.

Examples

			{1},
{1, 1},
{1, 3, 1},
{1, 11, 11, 1},
{1, 37, 101, 37, 1},
{1, 117, 473, 473, 117, 1},
{1, 359, -467, -10331, -467, 359, 1},
{1, 1087, -38805, -666047, -666047, -38805, 1087, 1},
{1, 3273, -564647, -22609991, -71238207, -22609991, -564647, 3273, 1},
{1, 9833, -6313279, -656760847, -6104652967, -6104652967, -656760847, -6313279, 9833, 1},
{1, 29515, -63520279, -18148426855, -499870912759, -1504945075459, -499870912759, -18148426855, -63520279, 29515, 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=3;

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