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 A337992 #11 Jan 10 2024 13:14:53
%S A337992 1,10,70,448,2786,17140,104938,640720,3904738,23762140,144429770,
%T A337992 876959896,5319995474,32247562084,195332428970,1182430057888,
%U A337992 7153644523970,43256701913260,261441118446154,1579452451096168,9538212470700466,57579647214814900,347476026056519210
%N A337992 a(n) = Sum_{k=0..n} (n+1)*2^(n+k)*hypergeom([-n, k-n+1], [2], 1/2). Row sums of A337617.
%F A337992 a(n) = Sum_{k=0..n} (if (n = k) then 2^n*(2^(n + 1) - 1) else 2^(2*k + 1)*Sum(j, 0..n - k)_ (-1)^j*2^(n - k - j)*binomial(n + 1, j)*binomial(2*n - j - k, n)). - _Detlef Meya_, Jan 09 2024
%F A337992 a(n) ~ 2^n * 3^(n+1). - _Vaclav Kotesovec_, Jan 10 2024
%t A337992 a[n_] := Sum[If[n==k, 2^n*(2^(n + 1) - 1), 2^(2*k + 1)*Sum[(-1)^j*2^(n - k - j)*Binomial[n + 1, j]*Binomial[2*n - j - k, n],{j, 0, n-k}]],{k, 0, n}]; Flatten[Table[a[n], {n, 0, 22}]] (* _Detlef Meya_, Jan 09 2024 *)
%Y A337992 Cf. A337617.
%K A337992 nonn
%O A337992 0,2
%A A337992 _Peter Luschny_, Oct 19 2020