Deteminant of the n x n symmetric matrix whose lower triangular part is the binomial numbers mod 2.
0, -1, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2
1
Sequence S000383 gives the conjectured locations of the 2 terms.
T. D. Noe, Plot of 343 terms
T. D. Noe, Table of 343 terms
Thomas Koshy, Triangular Arrays with Applications, Oxford, 2011, p. 171.
(Mma) Table[m = Table[0, {i, nn}, {j, nn}]; Do[m[[i+2, j+1]] = m[[j+1, i+2]] = Mod[Binomial[i, j], 2], {i, 0, nn - 2}, {j, 0, i}]; Det[m], {nn, 87}]
Cf. S000383.
sign
T. D. Noe, Nov 24 2014