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 A374428 #8 Aug 12 2024 13:29:05
%S A374428 1,1,3,2,5,13,6,14,33,79,24,54,122,277,633,120,264,582,1286,2849,6331,
%T A374428 720,1560,3384,7350,15986,34821,75973,5040,10800,23160,49704,106758,
%U A374428 229502,493825,1063623,40320,85680,182160,387480,824664,1756086,3741674,7977173,17017969
%N A374428 Triangle read by rows: T(n, k) = n! * 2^k * hypergeom([-k], [-n], 1/2).
%F A374428 T(n, k) = Sum_{j=0..k} 2^(k - j)*binomial(k, k - j)*(n - j)!. - _Detlef Meya_, Aug 12 2024
%t A374428 T[n_, k_] := n! 2^k Hypergeometric1F1[-k, -n, 1/2];
%t A374428 (* Alternative: *)
%t A374428 T[n_, k_] := Sum[2^(k - j)*Binomial[k, k - j]*((n - j)!), {j, 0, k}];
%t A374428 Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* _Detlef Meya_, Aug 12 2024 *)
%Y A374428 Cf. A010844 (main diagonal), A374427.
%K A374428 nonn,tabl
%O A374428 0,3
%A A374428 _Peter Luschny_, Jul 28 2024