A260638 Irregular table: list of symmetric n X n matrices made from 2-binomial coefficients, read by rows, where the k-th row of any n X n matrix is filled with binomial coefficients [k-1,k-1]..[k+n-2,k-1] (for q=2).

1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 7, 1, 7, 35, 1, 1, 1, 1, 1, 3, 7, 15, 1, 7, 35, 155, 1, 15, 155, 1395, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 1, 7, 35, 155, 651, 1, 15, 155, 1395, 11811, 1, 31, 651, 11811, 200787, 1, 1, 1, 1, 1, 1, 1, 3, 7, 15, 31, 63, 1, 7, 35, 155

Offset: 1

Author

Arkadiusz Wesolowski, Nov 11 2015

Keywords

• nonn
• easy
• tabf

Comments

The determinant of the n X n matrix is 2^((n/6)*(2*n^2 - 3*n + 1)), that is, A185995(n-1).

The permanent is in A260639.

Examples

			The irregular table starts:
1;
1, 1;
1, 3;
1, 1, 1;
1, 3, 7;
1, 7, 35;
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..819

Crossrefs

Cf. A000225, A006095, A185995, A260639.

Programs

Mathematica

Flatten@Flatten@Table[Table[QBinomial[r + c, r, 2], {r, 0, n}, {c, 0, n}], {n, 0, 5}]