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 A344556 #7 May 24 2021 23:34:04
%S A344556 1,1,5,34,315,3741,54531,944035,18934763,431773963,11030464423,
%T A344556 312023972228,9680623848325,326823162461823,11926991260987869,
%U A344556 467837288974848642,19628089812933434547,877052336082168698715,41581946832665768549007,2084818230218269733957646
%N A344556 a(n) = [x^n] 2 / (1 - (2*n - 1)*x + sqrt(1 - 2*x - 3*x^2)).
%C A344556 Main diagonal of A344567.
%F A344556 a(n) = Sum_{j=0..n} (n - 1)^j*binomial(n, j)*hypergeom([(j - n)/2, (j - n + 1)/2], [j + 2], 4).
%F A344556 a(n) ~ n^n * (1 + 1/n + 1/(2*n^2) - 4/(3*n^3) - 119/(24*n^4) - 1249/(120*n^5) - ...). - _Vaclav Kotesovec_, May 24 2021
%p A344556 aList := proc(len) 2 / (1 - (2*n - 1)*x + sqrt(1 - 2*x - 3*x^2));
%p A344556 seq(coeff(series(%, x, len+2), x, n), n = 0..len) end: aList(19);
%t A344556 Unprotect[Power]; 0^0 := 1;
%t A344556 a[n_] := Sum[(n-1)^j Binomial[n, j] Hypergeometric2F1[(j - n)/2, (j - n + 1)/2, j + 2, 4], {j, 0, n}]; Table[a[n], {n, 0, 19}]
%Y A344556 Cf. A344567.
%K A344556 nonn
%O A344556 0,3
%A A344556 _Peter Luschny_, May 24 2021