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 A343890 #14 May 03 2021 08:31:55
%S A343890 1,3,-1,20,-10,1,210,-126,21,-1,3024,-2016,432,-36,1,55440,-39600,
%T A343890 9900,-1100,55,-1,1235520,-926640,257400,-34320,2340,-78,1,32432400,
%U A343890 -25225200,7567560,-1146600,95550,-4410,105,-1,980179200,-784143360,249500160,-41583360,3998400,-228480,7616,-136,1
%N A343890 Coefficient triangle of generalized Laguerre polynomials n!*L(n,n+1,x) (rising powers of x).
%H A343890 Wikipedia, <a href="https://en.wikipedia.org/wiki/Laguerre_polynomials">Laguerre polynomials</a>
%H A343890 <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>
%F A343890 T(n, k) = (-1)^k * n! * binomial(2*n+1,n-k)/k! = (-1)^k * (2*n+1)! * binomial(n,k)/(k+n+1)!.
%e A343890 The triangle begins:
%e A343890 1;
%e A343890 3, -1;
%e A343890 20, -10, 1;
%e A343890 210, -126, 21, -1;
%e A343890 3024, -2016, 432, -36, 1;
%e A343890 55440, -39600, 9900, -1100, 55, -1;
%e A343890 1235520, -926640, 257400, -34320, 2340, -78, 1;
%t A343890 T[n_, k_] := (-1)^k * (2*n + 1)! * Binomial[n, k]/(k + n + 1)!; Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* _Amiram Eldar_, May 03 2021 *)
%o A343890 (PARI) T(n, k) = (-1)^k*(2*n+1)!*binomial(n,k)/(k+n+1)!;
%o A343890 (PARI) row(n) = Vecrev(n!*pollaguerre(n, n+1));
%Y A343890 Row sums (signed) give A343896, row sums (unsigned) give A343832.
%Y A343890 Cf. A343861.
%K A343890 sign,tabl
%O A343890 0,2
%A A343890 _Seiichi Manyama_, May 03 2021