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 A184173 Triangle read by rows: T(n,k) is the sum of the k X k minors in the n X n Pascal matrix (0<=k<=n; the empty 0 X 0 minor is defined to be 1). 0
 1, 1, 1, 1, 3, 1, 1, 7, 7, 1, 1, 15, 34, 15, 1, 1, 31, 144, 144, 31, 1, 1, 63, 574, 1155, 574, 63, 1, 1, 127, 2226, 8526, 8526, 2226, 127, 1, 1, 255, 8533, 60588, 113832, 60588, 8533, 255, 1, 1, 511, 32587, 424117, 1444608, 1444608, 424117, 32587, 511, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Apparently, the sum of the entries in row n is A005157(n). LINKS Alois P. Heinz, Rows n = 0..12, flattened Wikipedia, Minor (linear algebra) FORMULA The triangle is symmetric: T(n,k) = T(n,n-k). EXAMPLE T(3,1) = 7 because in the 3 X 3 Pascal matrix [1,0,0/1,1,0/1,2,1] the sum of the entries is 7. Triangle starts:   1;   1,  1;   1,  3,  1;   1,  7,  7,  1;   1, 15, 34, 15, 1; MAPLE with(combinat): with(LinearAlgebra): T:= proc(n, k) option remember; `if`(n-k add(add(       Determinant(SubMatrix(Matrix(n, (i, j)-> binomial(i-1, j-1)),        i, j)), j in l), i in l))(choose([\$1..n], k)))     end: seq(seq(T(n, k), k=0..n), n=0..7);  # Alois P. Heinz, Feb 11 2019 CROSSREFS Columns k=0-2 give: A000012, A000225, A306376. Cf. A005157, A007318. Sequence in context: A157152 A136126 A046802 * A022166 A141689 A058669 Adjacent sequences:  A184170 A184171 A184172 * A184174 A184175 A184176 KEYWORD nonn,tabl,changed AUTHOR Emeric Deutsch, Jan 12 2011 EXTENSIONS Typo corrected by Alois P. Heinz, Feb 11 2019 STATUS approved

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Last modified February 16 12:48 EST 2019. Contains 320163 sequences. (Running on oeis4.)