%I #20 Apr 26 2024 07:58:23
%S 1,1,1,1,2,1,1,3,4,2,1,1,4,9,10,7,2,1,1,5,17,36,46,30,14,4,2,1,1,6,28,
%T 97,219,281,226,116,45,18,5,1,1,1,7,43,226,872,2104,3170,2927,1774,
%U 793,290,87,37,9,3,2,1,1,8,62,472,2966,12882,36595,63842,69294,48881,24939,9808,3387,1059,313,107,37,9,4,1,1
%N Irregular triangle read by rows: T(n,k) is the number of unlabeled n-node graphs with intersection number (or edge clique cover number) k; n >= 1, 0 <= k <= floor(n^2/4).
%H Eric W. Weisstein, <a href="/A355754/b355754.txt">Table of n, a(n) for n = 1..108</a>
%H Paul Erdős, A. W. Goodman, and Louis Pósa, <a href="https://doi.org/10.4153%2FCJM-1966-014-3">The representation of a graph by set intersections</a>, Canadian Journal of Mathematics 18 (1966), 106-112.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IntersectionNumber.html">Intersection Number</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Intersection_number_(graph_theory)">Intersection number</a>
%F T(n,0) = 1.
%F T(n,1) = n-1.
%F T(n,2) = floor((n-2)*(2*n^2+7*n-12)/24) = A005744(n-2) = (4*n^3+6*n^2-52*n+45+3*(-1)^n)/48.
%e Triangle begins:
%e n\k | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
%e ----+--------------------------------------------------------------
%e 1 | 1
%e 2 | 1 1
%e 3 | 1 2 1
%e 4 | 1 3 4 2 1
%e 5 | 1 4 9 10 7 2 1
%e 6 | 1 5 17 36 46 30 14 4 2 1
%e 7 | 1 6 28 97 219 281 226 116 45 18 5 1 1
%e 8 | 1 7 43 226 872 2104 3170 2927 1774 793 290 87 37 9 3 2 1
%Y Cf. A000088 (row sums), A355755.
%K nonn,tabf
%O 1,5
%A _Pontus von Brömssen_, Jul 16 2022