%I #10 Mar 12 2024 18:37:11

%S 1,1,2,6,27,173,1464,15414,193901,2834337,47182518,880910414,

%T 18225754839,413835006621,10230048547292,273473280803598,

%U 7860479860630329,241731205891735649,7919436892637421066,275351783014543431222,10126387847107625874803,392728180939713131370669

%N a(n) = Sum_{k=0..n} 2^(n - k)*Pochhammer(k/2, n - k). Row sums of A370419(n - k, k).

%F From _Vaclav Kotesovec_, Mar 12 2024: (Start)

%F 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 a(n) ~ 2^(n - 1/2) * n^(n-1) / exp(n) * (1 + sqrt(Pi)/(2*sqrt(n))). (End)

%t a[n_] := Sum[2^(n - k)*Pochhammer[k/2, n - k], {k, 0, n}]; Array[a, 22, 0] (* _Hugo Pfoertner_, Mar 06 2024 *)

%Y Cf. A370419, A371079, A000522.

%K nonn

%O 0,3

%A _Peter Luschny_, Mar 06 2024