A176467 A symmetrical triangle:q=2;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, 4, 1, 1, 17, 17, 1, 1, 62, 196, 62, 1, 1, 207, 1528, 1528, 207, 1, 1, 660, 9893, 22154, 9893, 660, 1, 1, 2053, 57991, 247913, 247913, 57991, 2053, 1, 1, 6298, 320818, 2388134, 4474228, 2388134, 320818, 6298, 1, 1, 19163, 1712906, 20919938

Offset: 0

Author

Roger L. Bagula, Apr 18 2010

Keywords

• nonn
• tabl
• uned

Comments

Row sums are:

{1, 2, 6, 36, 322, 3472, 43262, 615916, 9904730, 177511112, 3486135606,...}.

Examples

			{1},
{1, 1},
{1, 4, 1},
{1, 17, 17, 1},
{1, 62, 196, 62, 1},
{1, 207, 1528, 1528, 207, 1},
{1, 660, 9893, 22154, 9893, 660, 1},
{1, 2053, 57991, 247913, 247913, 57991, 2053, 1},
{1, 6298, 320818, 2388134, 4474228, 2388134, 320818, 6298, 1},
{1, 19163, 1712906, 20919938, 66103548, 66103548, 20919938, 1712906, 19163, 1},
{1, 58016, 8941891, 171953190, 853179296, 1417870818, 853179296, 171953190, 8941891, 58016, 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=2;

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