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proposed
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proposed
nmax = 76;
a[n_] := 2^(n(n-1)/2)*n!*SeriesCoefficient[Sum[x^i/(2^(i(i-1)/2)*i!), {i, 0, nmax}]^n, {x, 0, n}];
Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, May 28 2024 *)
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Alois P. Heinz, <a href="/A372920/b372920_1.txt">Table of n, a(n) for n = 0..76</a>
editing
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Alois P. Heinz, <a href="/A372920/b372920_1.txt">Table of n, a(n) for n = 0..76</a>
a(n) = A322280(n,n).
a(n) == n (mod 2) for n >= 1.
Cf. A000035.