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 A370982 #10 Mar 12 2024 18:37:11
%S A370982 1,1,2,6,27,173,1464,15414,193901,2834337,47182518,880910414,
%T A370982 18225754839,413835006621,10230048547292,273473280803598,
%U A370982 7860479860630329,241731205891735649,7919436892637421066,275351783014543431222,10126387847107625874803,392728180939713131370669
%N A370982 a(n) = Sum_{k=0..n} 2^(n - k)*Pochhammer(k/2, n - k). Row sums of A370419(n - k, k).
%F A370982 From _Vaclav Kotesovec_, Mar 12 2024: (Start)
%F A370982 Recurrence: (n-4)*a(n) = (4*n^2 - 24*n + 33)*a(n-1) - (2*n - 5)*(2*n^2 - 12*n + 17)*a(n-2) + (4*n^3 - 40*n^2 + 134*n - 151)*a(n-3) - (n-3)*(2*n - 7)*a(n-4).
%F A370982 a(n) ~ 2^(n - 1/2) * n^(n-1) / exp(n) * (1 + sqrt(Pi)/(2*sqrt(n))). (End)
%t A370982 a[n_] := Sum[2^(n - k)*Pochhammer[k/2, n - k], {k, 0, n}]; Array[a, 22, 0] (* _Hugo Pfoertner_, Mar 06 2024 *)
%Y A370982 Cf. A370419, A371079, A000522.
%K A370982 nonn
%O A370982 0,3
%A A370982 _Peter Luschny_, Mar 06 2024