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 A046900 #21 Apr 18 2023 09:19:16
%S A046900 1,-1,1,1,-3,2,1,3,-10,6,-1,9,10,-42,24,-17,21,50,42,-216,120,-107,
%T A046900 -33,230,294,216,-1320,720,-415,-1173,670,1974,1944,1320,-9360,5040,
%U A046900 1231,-13515,-4510,11130,17064,14520,9360,-75600,40320,56671,-113739,-131230,20202,136296,157080,121680,75600
%N A046900 Triangle inverse to that in A046899.
%C A046900 Sequence gives numerators; denominators are A001813.
%D A046900 H. W. Gould, A class of binomial sums and a series transform, Utilitas Math., 45 (1994), 71-83.
%H A046900 H. W. Gould, <a href="/A007680/a007680.pdf">A class of binomial sums and a series transform</a>, Utilitas Math., 45 (1994), 71-83. (Annotated scanned copy)
%e A046900 1; -1/2 1/2; 1/12 -3/12 2/12; ...
%p A046900 with(linalg): b:=proc(n,k) if k<=n then binomial(n+k,k) else 0 fi end: bb:=(n,k)->b(n-1,k-1): B:=matrix(12,12,bb): A:=inverse(B): a:=(n,k)->((2*n-2)!/(n-1)!)*A[n,k]: for n from 0 to 10 do seq(a(n,k),k=1..n) od; # yields sequence in triangular form - _Emeric Deutsch_
%t A046900 max = 10; b[n_, k_] := If[k <= n, Binomial[n+k, k], 0]; BB = Table[b[n, k], {n, 0, max-1}, {k, 0, max-1}]; AA = Inverse[BB]; a[n_, k_] := ((2n-2)!/(n-1)!)*AA[[n, k]]; Flatten[ Table[ a[n, k], {n, 1, max}, {k, 1, n}]] (* _Jean-François Alcover_, Aug 08 2012, after _Emeric Deutsch_ *)
%Y A046900 Cf. A001813, A046899.
%K A046900 sign,tabl,easy,nice
%O A046900 0,5
%A A046900 _N. J. A. Sloane_
%E A046900 More terms from _Emeric Deutsch_, Jun 25 2005