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 A136214 #24 Sep 08 2022 08:45:32
%S A136214 1,1,1,4,4,1,28,28,7,1,280,280,70,10,1,3640,3640,910,130,13,1,58240,
%T A136214 58240,14560,2080,208,16,1,1106560,1106560,276640,39520,3952,304,19,1,
%U A136214 24344320,24344320,6086080,869440,86944,6688,418,22,1
%N A136214 Triangle U, read by rows, where U(n,k) = Product_{j=k..n-1} (3*j+1) for n > k with U(n,n) = 1.
%C A136214 Let G(m, k, p) = (-p)^k*Product_{j=0..k-1}(j - m - 1/p) and T(n, k, p) = G(n-1, n-k, p) then T(n, k, 1) = A094587(n, k), T(n, k, 2) = A112292(n, k) and T(n, k, 3) is this sequence. - _Peter Luschny_, Jun 01 2009, revised Jun 18 2019
%H A136214 G. C. Greubel, <a href="/A136214/b136214.txt">Rows n = 0..100 of triangle, flattened</a>
%F A136214 Matrix powers: column 0 of U^(k+1) = column k of A136216 for k >= 0; simultaneously, column k = column 0 of A136216^(3k+1) for k >= 0. Element in column 0, row n, of matrix power U^(k+1) = A007559(n)*C(n+k,k), where A007559 are triple factorials found in column 0 of this triangle.
%e A136214 Triangle begins:
%e A136214 1;
%e A136214 1, 1;
%e A136214 4, 4, 1;
%e A136214 28, 28, 7, 1;
%e A136214 280, 280, 70, 10, 1;
%e A136214 3640, 3640, 910, 130, 13, 1;
%e A136214 58240, 58240, 14560, 2080, 208, 16, 1;
%e A136214 1106560, 1106560, 276640, 39520, 3952, 304, 19, 1; ...
%e A136214 Matrix inverse begins:
%e A136214 1;
%e A136214 -1, 1;
%e A136214 0, -4, 1;
%e A136214 0, 0, -7, 1;
%e A136214 0, 0, 0, -10, 1;
%e A136214 0, 0, 0, 0, -13, 1; ...
%p A136214 nmax:=8; for n from 0 to nmax do U(n, n):=1 od: for n from 0 to nmax do for k from 0 to n do if n > k then U(n, k) := mul((3*j+1), j = k..n-1) fi: od: od: for n from 0 to nmax do seq(U(n, k), k=0..n) od: seq(seq(U(n, k), k=0..n), n=0..nmax); # _Johannes W. Meijer_, Jul 04 2011, revised Nov 23 2012
%t A136214 Table[Product[3*j+1, {j,k,n-1}], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Jun 14 2019 *)
%o A136214 (PARI) T(n,k)=if(n==k,1,prod(j=k,n-1,3*j+1))
%o A136214 (Magma) [[n eq 0 select 1 else k eq n select 1 else (&*[3*j+1: j in [k..n-1]]): k in [0..n]]: n in [0..12]]; // _G. C. Greubel_, Jun 14 2019
%o A136214 (Sage)
%o A136214 def T(n, k):
%o A136214 if (k==n): return 1
%o A136214 else: return product(3*j+1 for j in (k..n-1))
%o A136214 [[T(n, k) for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, Jun 14 2019
%Y A136214 Cf. A094587, A112333, A136216, A136239; A007559, A136212, A136213.
%K A136214 nonn,tabl
%O A136214 0,4
%A A136214 _Paul D. Hanna_, Feb 07 2008