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 A111534 #8 Aug 09 2018 05:56:00
%S A111534 1,1,4,33,416,7045,149472,3804353,112784896,3812791581,144643185600,
%T A111534 6081135558817,280510445260800,14080668974435141,763890295406672896,
%U A111534 44529851124925034625,2775373003913373810688,184147301185264051623181
%N A111534 Main diagonal of table A111528.
%C A111534 For n>0, a(n) is divisible by n: a(n)/n = A111535(n).
%F A111534 a(n) = [x^n] Log( Sum_{m=0..n} (n-1+m)!/(n-1)!*x^m ).
%t A111534 T[n_, k_] := T[n, k] = Which[n<0 || k<0, 0, k==0 || k==1, 1, n==0, k!, True, (T[n-1, k+1]-T[n-1, k])/n - Sum[T[n, j] T[n-1, k-j], {j, 1, k-1}]];
%t A111534 a[n_] := T[n, n];
%t A111534 Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Aug 09 2018 *)
%o A111534 (PARI) {a(n)=if(n<0,0,if(n==0,1, polcoeff(log(sum(m=0,n,(n-1+m)!/(n-1)!*x^m)),n)))}
%Y A111534 Cf: A111528 (table), A003319 (row 1), A111529 (row 2), A111530 (row 3), A111531 (row 4), A111532 (row 5), A111533 (row 6).
%K A111534 nonn
%O A111534 0,3
%A A111534 _Paul D. Hanna_, Aug 06 2005