This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A198261 #16 May 31 2025 05:20:21
%S A198261 1,0,1,1,0,1,4,3,0,1,41,16,6,0,1,768,205,40,10,0,1,27449,4608,615,80,
%T A198261 15,0,1,1887284,192143,16128,1435,140,21,0,1,252522481,15098272,
%U A198261 768572,43008,2870,224,28,0,1
%N A198261 Triangular array read by rows T(n,k) is the number of simple labeled graphs on n nodes with exactly k isolated nodes, 0<=k<=n.
%C A198261 Row sums = 2^binomial(n,2) = A006125(n).
%C A198261 First column (k=0) is A006129.
%F A198261 E.g.f. for column k: x^k/k! *A(x)/exp(x) where A(x) is the e.g.f. for A006125.
%F A198261 T(n,n) = 1 (the empty graph). - _Geoffrey Critzer_, Nov 11 2011
%F A198261 T(n,n-1) = 0. - _Geoffrey Critzer_, Nov 11 2011
%e A198261 Triangle begins:
%e A198261 1;
%e A198261 0, 1;
%e A198261 1, 0, 1;
%e A198261 4, 3, 0, 1;
%e A198261 41, 16, 6, 0, 1;
%e A198261 768, 205, 40, 10, 0, 1;
%e A198261 27449, 4608, 615, 80, 15, 0, 1;
%e A198261 1887284, 192143, 16128, 1435, 140, 21, 0, 1;
%t A198261 g=Sum[2^Binomial[n, 2]x^n/n!, {n, 0, 20}]; Transpose[Table[Range[0, 10]! CoefficientList[Series[(x^n/n!)( g/Exp[x]), {x, 0, 10}], x], {n, 0, 8}]]//Grid
%Y A198261 Cf. A006125, A006129.
%K A198261 nonn,tabl
%O A198261 0,7
%A A198261 _Geoffrey Critzer_, Oct 22 2011