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 A215863 #8 Dec 04 2014 07:04:01 %S A215863 0,19,135,540,1610,3990,8694,17220,31680,54945,90805,144144,221130, %T A215863 329420,478380,679320,945744,1293615,1741635,2311540,3028410,3920994, %U A215863 5022050,6368700,8002800,9971325,12326769,15127560,18438490,22331160,26884440,32184944,38327520 %N A215863 Number of simple labeled graphs on n+3 nodes with exactly n connected components that are trees or cycles. %H A215863 Alois P. Heinz, <a href="/A215863/b215863.txt">Table of n, a(n) for n = 0..1000</a> %F A215863 G.f.: (6*x^2-2*x-19)*x/(x-1)^7. %F A215863 a(n) = C(n+3,4)*(n^2+13*n+24)/2. %e A215863 a(1) = 19: %e A215863 .1-2. .1-2. .1 2. .1-2. .1-2. .1 2. .1 2. .1 2. .1-2. .1-2. %e A215863 .| |. . X . .|X|. .|\ . . /|. . \|. .|/ . .| |. .| . .| |. %e A215863 .4-3. .4-3. .4.3. .4.3. .4.3. .4-3. .4-3. .4-3. .4-3. .4.3. %e A215863 . %e A215863 .1-2. .1 2. .1-2. .1-2. .1-2. .1 2. .1 2. .1 2. .1 2. %e A215863 . |. . X . . / . . \ . . X . .|/|. . X|. .|X . .|\|. %e A215863 .4-3. .4-3. .4-3. .4-3. .4.3. .4.3. .4.3. .4.3. .4.3. %p A215863 a:= n-> binomial(n+3,4)*(24+(13+n)*n)/2: %p A215863 seq(a(n), n=0..40); %Y A215863 A diagonal of A215861. %K A215863 nonn %O A215863 0,2 %A A215863 _Alois P. Heinz_, Aug 25 2012