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a(n) is the constant term in expansion of Product_{k=1..n} (x^(k^4) + 1 + 1/x^(k^4)).
3

%I #15 Jan 22 2024 05:55:42

%S 1,1,1,1,1,1,1,1,1,3,3,15,25,59,109,227,525,1321,2917,7085,15893,

%T 38759,90179,223933,534867,1339691,3246961,8296441,20426971,52715563,

%U 131480623,342491253,864759837,2270860455,5793103989,15316065497,39429185075,105008858223

%N a(n) is the constant term in expansion of Product_{k=1..n} (x^(k^4) + 1 + 1/x^(k^4)).

%t Table[Coefficient[Product[x^(k^4) + 1 + 1/x^(k^4), {k, 1, n}], x, 0], {n, 0, 25}]

%Y Cf. A000583, A007576, A158465, A350249.

%K nonn

%O 0,10

%A _Ilya Gutkovskiy_, Jan 21 2024

%E a(26)-a(37) from _Alois P. Heinz_, Jan 21 2024