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 A100620 #6 Jan 16 2013 09:08:33
%S A100620 0,1,1,1,7,19,41,751,989,2857,16067,434293,1364651,8181904909,
%T A100620 90241897,5044289,15043611773,5026792806787,203732352169,
%U A100620 69028763155644023,1145302367137,1022779523247467,396760150748100749,750218743980105669781,35200969735190093
%N A100620 Numerator of Cotesian number C(n,0).
%D A100620 Charles Jordan, Calculus of Finite Differences, Chelsea 1965, p. 513.
%e A100620 0, 1/2, 1/6, 1/8, 7/90, 19/288, 41/840, 751/17280, 989/28350, 2857/89600, 16067/598752, 434293/17418240, 1364651/63063000, 8181904909/402361344000, ... = A100620/A100621 = A002177/A002176 (the latter is not in lowest terms)
%p A100620 (This defines the Cotesian numbers C(n,i)) with(combinat); C:=proc(n,i) if i=0 or i=n then RETURN( (1/n!)*add(n^a*stirling1(n,a)/(a+1),a=1..n+1) ); fi; (1/n!)*binomial(n,i)* add( add( n^(a+b)*stirling1(i,a)*stirling1(n-i,b)/((b+1)*binomial(a+b+1,b+1)), b=1..n-i+1), a=1..i+1); end;
%t A100620 cn[n_, 0] := Sum[n^j*StirlingS1[n, j]/(j + 1), {j, 1, n + 1}]/n!; cn[n_, n_] := cn[n, 0]; cn[n_, k_] := 1/n!*Binomial[n, k]*Sum[n^(j + m)*StirlingS1[k, j]*StirlingS1[n - k, m]/((m + 1)*Binomial[j + m + 1, m + 1]), {m, 1, n}, {j, 1, k + 1}]; Table[cn[n, 0] // Numerator, {n, 0, 24}] (* _Jean-François Alcover_, Jan 16 2013 *)
%Y A100620 See A002176 for further references. A diagonal of A100640/A100641.
%K A100620 nonn,frac
%O A100620 0,5
%A A100620 _N. J. A. Sloane_, Dec 04 2004