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A083029
Triangle read by rows: T(n,k), n >=1, 0 <= k <= C(n,k), = number of n X n symmetric positive semi-definite matrices with 2's on the main diagonal and 1's and 0's elsewhere and with k 1's above the diagonal.
9
1, 1, 1, 1, 3, 3, 1, 1, 6, 15, 20, 15, 6, 1, 1, 10, 45, 120, 210, 192, 200, 90, 45, 10, 1, 1, 15, 105, 455, 1365, 2517, 3805, 3975, 3690, 2910, 1548, 975, 255, 105, 15, 1, 1, 21, 210, 1330, 5985, 18207, 39557, 71235, 95130, 115115, 110670, 104265, 72520, 56070, 32445, 15862, 7434, 2730, 665, 210, 21, 1, 1, 28, 378, 3276, 20475, 91392, 288596, 692576, 1374597, 2161180, 3247622, 3740016, 4422915, 4117512, 3886200, 3044048, 2579780, 1591296, 1111768, 628600, 323148, 148184, 65576, 20160, 7105, 1540, 378, 28, 1
OFFSET
1,5
EXAMPLE
1;
1,1;
1,3,3,1;
1,6,15,20,15,6,1;
...
CROSSREFS
Rows sums give A085658.
A038379(n) = Sum_{k=0..C(n,2)} 2^k * T(n,k).
A084546 is an upper bound.
Sequence in context: A352472 A080858 A144228 * A084546 A288266 A174116
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Jul 13 2003
EXTENSIONS
Rows n=6..8 added by Max Alekseyev, Jun 05 2024
STATUS
approved