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

%I #7 Sep 22 2024 18:01:56

%S 2,16,384,19600,1734656,235929600,45619718144,11882195067136,

%T 4007380608000000,1698030663170523136,882712840220180480000,

%U 552231274155798665465856,409206182467603556470882304,354386995669969036902400000000,354633184176852764825029617647616

%N Obverse convolution (n^2 + n + 1)**(n^2 + n + 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; (sqrt(a(2k+1))) = (1, 35, 3840, 861764, 325771264, 185780662704...).

%F a(n) ~ n^(2*n+2) / exp(2*n - Pi*(n+1)/2). - _Vaclav Kotesovec_, Sep 22 2024

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

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

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

%Y Cf. A374848, A375058.

%K nonn

%O 0,1

%A _Clark Kimberling_, Sep 22 2024