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Obverse convolution (n^2 + 1)**(n^2 + 1); see Comments.
0

%I #10 Sep 20 2024 16:06:14

%S 2,9,144,5929,466560,59213025,10958689280,2771535732849,

%T 915539439919104,382088350057032025,196357891384811520000,

%U 121752085389995771825625,89582478947424173216497664,77138638421388109999960896369,76829768389915556918132736000000

%N Obverse convolution (n^2 + 1)**(n^2 + 1); see Comments.

%C See A374848 for the definition of obverse convolution and a guide to related sequences.

%C a(2k+1) is a square for k>=0.

%F a(n) ~ n^(2*n+2) / exp(2*n - Pi*n/2). - _Vaclav Kotesovec_, Sep 20 2024

%t s[n_] := n^2 + 1; t[n_] := n^2 + 1;

%t u[n_] := Product[s[k] + t[n - k], {k, 0, n}];

%t Table[u[n], {n, 0, 20}]

%Y Cf. A323540, A374848, A375051.

%K nonn

%O 0,1

%A _Clark Kimberling_, Sep 20 2024