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 A154594 #13 May 27 2024 09:25:15
%S A154594 1,-2,-2,4,26,4,-8,-186,-240,-8,16,1090,4524,2008,16,-32,-5866,-57992,
%T A154594 -85424,-16288,-32,64,30354,616452,2099504,1423968,130848,64,-128,
%U A154594 -154202,-5902944,-39122296,-61925632,-22159968,-1048064,-128,256,776642,53083228,619239464,1884138544,1615232096,331200832,8387456,256
%N A154594 Triangle read by rows: T(n, k) = [x^k] p(x, n), where p(x, n) = (-1)^n*(1 - 2*x)^(n + 1)* Sum_{j >= 0} (3*j + 2)^n*(2*x)^j.
%H A154594 G. C. Greubel, <a href="/A154594/b154594.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A154594 T(n, k) = [x^k]( p(x, n) ), where p(x, n) = (-1)^n*(1-2*x)^(n+1)*Sum_{j >= 0} (3*j+2)^n*(2*x)^j, or p(x, n) = (-2)^n * (1-2*x)^(n+1) * LerchPhi(2*x, -n, 2/3).
%F A154594 Sum_{k=0..n} T(n, k) = A151919(n) (row sums).
%e A154594 Triangle begins as:
%e A154594 1;
%e A154594 -2, -2;
%e A154594 4, 26, 4;
%e A154594 -8, -186, -240, -8;
%e A154594 16, 1090, 4524, 2008, 16;
%e A154594 -32, -5866, -57992, -85424, -16288, -32;
%e A154594 64, 30354, 616452, 2099504, 1423968, 130848, 64;
%e A154594 -128, -154202, -5902944, -39122296, -61925632, -22159968, -1048064, -128;
%t A154594 m=12; p[x_, n_]= (-1)^n*(1-2*x)^(n+1)*Sum[(3*j+2)^n*(2*x)^j, {j,0,m+2}];
%t A154594 T[n_, k_]:= Coefficient[Series[p[x, n], {x,0,n}], x, k];
%t A154594 Table[T[n,k], {n,0,m}, {k,0,n}]//Flatten
%o A154594 (Magma)
%o A154594 m:=12;
%o A154594 R<x>:=PowerSeriesRing(Integers(), m+2);
%o A154594 p:= func< n,x | (-1)^n*(1-2*x)^(n+1)*(&+[(3*j+2)^n*(2*x)^j: j in [0..n]]) >;
%o A154594 T:= func< n,k | Coefficient(R!( p(n,x) ), k) >;
%o A154594 [T(n,k): k in [0..n], n in [0..m]]; // _G. C. Greubel_, May 26 2024
%o A154594 (SageMath)
%o A154594 m=12
%o A154594 def p(x,n): return (-1)^n*(1-2*x)^(n+1)*sum((3*j+2)^n*(2*x)^j for j in range(n+1))
%o A154594 def T(n,k): return ( p(x,n) ).series(x, n+1).list()[k]
%o A154594 flatten([[T(n,k) for k in range(n+1)] for n in range(m+1)]) # _G. C. Greubel_, May 26 2024
%Y A154594 Cf. A151919 (row sums), A154593.
%K A154594 sign,tabl
%O A154594 0,2
%A A154594 _Roger L. Bagula_, Jan 12 2009
%E A154594 Edited by _G. C. Greubel_, May 26 2024