A140818 Coefficients of Hodge diamond binomial 'X' matrices as polynomials: matrix example; M={{1,0,1}. {0,2,0], {1,0,1}: M(d, x, y)= Sum[Sum[If[n == m, Binomial[d - 1, m - 1], If[n == d - m + 1, Binomial[d - 1, n - 1], 0]]*x^(n - 1)*y^(m - 1), {n, 1, d}], {m, 1, d}] .

1, 2, 2, 2, 2, 2, 2, 6, 6, 2, 2, 8, 6, 8, 2, 2, 10, 20, 20, 10, 2, 2, 12, 30, 20, 30, 12, 2, 2, 14, 42, 70, 70, 42, 14, 2, 2, 16, 56, 112, 70, 112, 56, 16, 2, 2, 18, 72, 168, 252, 252, 168, 72, 18, 2

Offset: 1

Author

Roger L. Bagula and Mats Granvik, Jul 16 2008

Keywords

• nonn
• tabl
• uned

Comments

Apparently the same as A139813. - Georg Fischer, Nov 02 2018

Examples

			{1},
{2, 2},
{2, 2, 2},
{2, 6, 6, 2},
{2, 8, 6, 8, 2},
{2, 10, 20, 20, 10, 2},
{2, 12, 30, 20, 30, 12, 2},
{2, 14, 42, 70, 70, 42, 14, 2},
{2, 16, 56, 112, 70, 112, 56, 16, 2},
{2, 18, 72, 168, 252, 252, 168, 72, 18, 2}.
		

Crossrefs

Cf. A139813, A140685.

Programs

Mathematica

M[d_, x_, y_] := Sum[Sum[If[n == m, Binomial[d - 1, m - 1], If[n == d - m + 1, Binomial[ d - 1, n - 1], 0]]*x^(n - 1)*y^(m - 1), {n, 1, d}], {m, 1, d}];
Flatten@ Table[CoefficientList[M[d, x, 1], x], {d, 1, 10}]