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Obverse convolution (floor(3n/2))**(floor(3n/2)); see Comments.
4

%I #6 Aug 02 2024 18:59:15

%S 0,1,18,256,5400,117649,3359232,100000000,3643149312,137858491849,

%T 6126151500000,281474976710656,14777503265582208,799006685782884121,

%U 48413259982080000000,3011361496339065143296,206882551397716479442944,14551915228366851806640625

%N Obverse convolution (floor(3n/2))**(floor(3n/2)); see Comments.

%C See A374848 for the definition of obverse convolution and a guide to related sequences. If k>=0, then a(2k) is even and a(2k+1) is a square.

%F a(n) ~ exp(-1/3) * (3*n/2)^(n+1). - _Vaclav Kotesovec_, Aug 02 2024

%t s[n_] := Floor[3 n/2]; t[n_] := Floor[3 n/2];

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

%t Table[u[n], {n, 0, 24}]

%Y Cf. A016789, A374848.

%K nonn

%O 0,3

%A _Clark Kimberling_, Jul 31 2024