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

%I #6 Sep 20 2024 02:18:47

%S -2,1,0,441,75264,14402025,3451797504,1043554187025,392874877255680,

%T 181193143212358641,100757479882752000000,66592039534109652160521,

%U 51648427918242896412672000,46486269540273907302519872025,48078115878910207012782666153984

%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 19 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. A005563, A323540, A374848, A375052.

%K sign

%O 0,1

%A _Clark Kimberling_, Sep 15 2024