A205457 Symmetric matrix, by antidiagonals: C(max(2i,2j),min(2i,2j)), i>=0, j>=0.

1, 1, 1, 1, 1, 1, 1, 6, 6, 1, 1, 15, 1, 15, 1, 1, 28, 15, 15, 28, 1, 1, 45, 70, 1, 70, 45, 1, 1, 66, 210, 28, 28, 210, 66, 1, 1, 91, 495, 210, 1, 210, 495, 91, 1, 1, 120, 1001, 924, 45, 45, 924, 1001, 120, 1, 1, 153, 1820, 3003, 495, 1, 495, 3003, 1820, 153, 1, 1

Offset: 1

Author

Clark Kimberling, Jan 28 2012

Keywords

• nonn
• tabl

Examples

			Northwest corner:
1....6....15...28...45
6....1....15...70...210
15...15...1....28...210
28...70...28...1....45
45...210..210..45...1
		

Crossrefs

Cf. A182878, A205456.

Programs

Mathematica

f[i_, j_] := Binomial[Max[2 i - 2, 2 j - 2], Min[2 i - 2, 2 j - 2]]
TableForm[Table[f[i, j], {i, 1, 10}, {j, 1, 10}]]
Flatten[Table[f[i, n + 1 - i], {n, 1, 14}, {i, 1, n}]]

Maxima

S(x,y):=((x^3-3*x^2)*y^3-x^2*y^2)/((x^2-2*x+1)*y^3+(-x^2-3)*y^2+(2*x+3)*y-1);
taylor((S(x,y)+S(y,x))/(x*y)-x*y/(1-x*y)+1/(1-x)+1/(1-y)-1,x,0,7,y,0,7); /* Vladimir Kruchinin, Oct 29 2020 */

Formula

G.f.: (S(x,y)+S(y,x))/(x*y)-x*y/(1-x*y)+1/(1-x)+1/(1-y)-1, where S(x,y)=((x^3-3*x^2)*y^3-x^2*y^2)/((x^2-2*x+1)*y^3+(-x^2-3)*y^2+(2*x+3)*y-1). - Vladimir Kruchinin, Oct 29 2020