%I #14 Feb 20 2020 11:40:34

%S 1,1,1,1,2,3,1,3,11,6,1,4,25,63,19,1,5,45,266,477,59,1,6,73,785,4646,

%T 5339,267,1,7,109,1908,26205,136935,94535,1380,1,8,155,4085,110140,

%U 1696407,7121703,2774240,9832,1,9,211,7992,384209,13779220,209046708,647596643,135794730,90842

%N Triangle read by rows: T(n,k) gives number of connected graphs on n nodes with clique number n-k, (n>=2, k=0..n-2).

%C This sequence can be derived from A263341 since the number of graphs with clique number <= k is the Euler transform of the number of connected graphs with clique number <= k. - _Andrew Howroyd_, Feb 19 2020

%H Andrew Howroyd, <a href="/A126744/b126744.txt">Table of n, a(n) for n = 2..79</a> (rows 2..13 derived from Brendan McKay data in A263341)

%H Keith M. Briggs, <a href="http://keithbriggs.info/cgt.html">Combinatorial Graph Theory</a>

%e Triangle begins:

%e n=...1...2...3...4....5....6.....7......8........9........10

%e k.------------------------------------------------------------

%e 2|...0...1...1...3....6...19....59....267.....1380......9832 = A024607

%e 3|...0...0...1...2...11...63...477...5339....94535...2774240 = A126745

%e 4|...0...0...0...1....3...25...266...4646...136935...7121703 = A126746

%e 5|...0...0...0...0....1....4....45....785....26205...1696407 = A126747

%e 6|...0...0...0...0....0....1.....5.....73.....1908....110140 = A126748

%e 7|...0...0...0...0....0....0.....1......6......109......4085 = A217987

%e 8|...0...0...0...0....0....0.....0......1........7.......155

%e ...

%e From _Andrew Howroyd_, Feb 19 2020: (Start)

%e As a triangle with columns being clique number >= 2:

%e 1;

%e 1, 1;

%e 3, 2, 1;

%e 6, 11, 3, 1;

%e 19, 63, 25, 4, 1;

%e 59, 477, 266, 45, 5, 1;

%e 267, 5339, 4646, 785, 73, 6, 1;

%e 1380, 94535, 136935, 26205, 1908, 109, 7, 1;

%e 9832, 2774240, 7121703, 1696407, 110140, 4085, 155, 8, 1;

%e ...

%e (End)

%Y Diagonals give A024607, A126745, A126746, A126747, A126748, A217987.

%Y Row sums are A001349.

%Y Cf. A263341.

%K nonn,tabl,hard

%O 2,5

%A _N. J. A. Sloane_, Feb 18 2007

%E Terms a(47) and beyond derived from A263341 added by _Andrew Howroyd_, Feb 19 2020