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 A336746 #7 Sep 05 2020 20:21:14
%S A336746 0,1,1,2,3,5,3,5,11,26,4,7,17,50,154,5,9,23,74,274,1044,6,11,29,98,
%T A336746 394,1764,8028,7,13,35,122,514,2484,13068,69264,8,15,41,146,634,3204,
%U A336746 18108,109584,663696,9,17,47,170,754,3924,23148,149904,1026576,6999840
%N A336746 Triangle read by rows: T(n,k) = (n-k-1+H(k+1))*((k+1)!) for 0 <= k <= n where H(k+1) = Sum_{i=0..k} 1/(i+1) for k >= 0.
%F A336746 T(n,k) = T(n,k-1) + k * T(n-1,k-1) for 0 < k <= n with initial values T(n,0) = n for n >= 0 and T(i,j) = 0 if j < 0 or j > i.
%F A336746 T(n,k) = k! + T(n-1,k-1) * (k+1) for 0 < k <= n.
%F A336746 T(n,k) = (k+1)! + T(n-1,k) for 0 <= k < n.
%F A336746 E.g.f. of main diagonal (case n=0) and n-th subdiagonal (n>0): Sum_{k>=0} T(n+k,k) * x^k / k! = (n - log(1-x)) / (1-x)^2 for n >= 0.
%F A336746 G.f. of column k>=0: Sum_{n>=k} T(n,k) * y^n = (T(k,k) * y^k + ((k+1)! - T(k,k)) * y^(k+1)) / (1-y)^2.
%F A336746 G.f.: Sum_{n>=0, k=0..n} T(n,k)*x^k*y^n/k! = (y - (1-y) * log(1-x*y)) / ((1-y)^2 * (1-x*y)^2).
%e A336746 The triangle starts:
%e A336746 n\k : 0 1 2 3 4 5 6 7 8 9
%e A336746 =================================================================
%e A336746 0 : 0
%e A336746 1 : 1 1
%e A336746 2 : 2 3 5
%e A336746 3 : 3 5 11 26
%e A336746 4 : 4 7 17 50 154
%e A336746 5 : 5 9 23 74 274 1044
%e A336746 6 : 6 11 29 98 394 1764 8028
%e A336746 7 : 7 13 35 122 514 2484 13068 69264
%e A336746 8 : 8 15 41 146 634 3204 18108 109584 663696
%e A336746 9 : 9 17 47 170 754 3924 23148 149904 1026576 6999840
%e A336746 ...
%Y A336746 Cf. A001477 (column 0), A005408 (column 1), A016969 (column 2), A001705 (main diagonal), A000254 (1st subdiagonal), A000774 (2nd subdiagonal).
%K A336746 nonn,easy,tabl
%O A336746 0,4
%A A336746 _Werner Schulte_, Aug 02 2020