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 A196347 #44 Sep 08 2022 08:45:59
%S A196347 1,1,1,2,4,2,6,18,18,6,24,96,144,96,24,120,600,1200,1200,600,120,720,
%T A196347 4320,10800,14400,10800,4320,720,5040,35280,105840,176400,176400,
%U A196347 105840,35280,5040,40320,322560,1128960,2257920,2822400,2257920,1128960,322560,40320
%N A196347 Triangle T(n, k) read by rows, T(n, k) = n!*binomial(n, k).
%C A196347 Unsigned version of A021012.
%C A196347 Equal to A136572*A007318.
%H A196347 G. C. Greubel, <a href="/A196347/b196347.txt">Table of n, a(n) for n = 0..495</a>
%H A196347 P. Bala, <a href="/A131689/a131689.pdf">Deformations of the Hadamard product of power series</a>
%H A196347 Paul Barry, <a href="https://arxiv.org/abs/2101.06713">On the inversion of Riordan arrays</a>, arXiv:2101.06713 [math.CO], 2021.
%H A196347 M. Dukes, C. D. White, <a href="http://arxiv.org/abs/1603.01589">Web Matrices: Structural Properties and Generating Combinatorial Identities</a>, arXiv:1603.01589 [math.CO], 2016.
%F A196347 T(n,k) is given by (1,1,2,2,3,3,4,4,5,5,6,6,...) DELTA (1,1,2,2,3,3,4,4,5,5,6,6, ...) where DELTA is the operator defined in A084938.
%F A196347 Sum_{k>=0} T(m,k)*T(n,k) = (m+n)!.
%F A196347 T(2n,n) = A122747(n).
%F A196347 Sum_{k>=0} T(n,k)^2 = A010050(n) = (2n)!.
%F A196347 Sum_{k>=0} T(n,k)*x^k = A000007(n), A000142(n), A000165(n), A032031(n), A047053(n), A052562(n), A047058(n), A051188(n), A051189(n), A051232(n), A051262(n), A196258(n), A145448(n) for x = -1,0,1,2,3,4,5,6,7,8,9,10,11 respectively.
%F A196347 The row polynomials have the form (x + 1) o (x + 2) o ... o (x + n), where o denotes the black diamond multiplication operator of Dukes and White. See example E10 in the Bala link. - _Peter Bala_, Jan 18 2018
%e A196347 Triangle begins:
%e A196347 1;
%e A196347 1, 1;
%e A196347 2, 4, 2;
%e A196347 6, 18, 18, 6;
%e A196347 24, 96, 144, 96, 24;
%e A196347 120, 600, 1200, 1200, 600, 120;
%e A196347 ...
%t A196347 Table[n!*Binomial[n, j], {n, 0, 30}, {j, 0, n}] (* _G. C. Greubel_, Sep 27 2015 *)
%o A196347 (Sage) factorial(n)*binomial(n,k) # _Danny Rorabaugh_, Sep 27 2015
%o A196347 (Magma) /* As triangle */ [[Factorial(n)*Binomial(n, k): k in [0..n]]: n in [0.. 15]]; // _Vincenzo Librandi_, Sep 28 2015
%Y A196347 Cf. A007318, A008619, A021012, A084938, A136572.
%Y A196347 Columns include: A000142, A001563, A001804, A001805, A001806, A001807.
%K A196347 nonn,tabl,easy
%O A196347 0,4
%A A196347 _Philippe Deléham_, Oct 28 2011
%E A196347 Name exchanged with a formula by _Peter Luschny_, Feb 01 2015