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A368348 a(n) = [x^(n^4)] Product_{k=1..n} (x^(k^4) + 1/x^(k^4)).

%I A368348 #28 Feb 14 2025 09:45:52
%S A368348 1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3,0,0,19,26,0,0,40,129,0,0,616,785,
%T A368348 0,0,4080,9309,0,0,44775,72659,0,0,430297,781505,0,0,3934457,7765047,
%U A368348 0,0,44740433,78818429,0,0,463089552,900950811,0,0,5344766190,9806206864,0,0
%N A368348 a(n) = [x^(n^4)] Product_{k=1..n} (x^(k^4) + 1/x^(k^4)).
%p A368348 b:= proc(n, i) option remember; (m-> `if`(n>m, 0, `if`(n=m, 1,
%p A368348       b(abs(n-i^4), i-1)+b(n+i^4, i-1))))(i*(i+1)*(2*i+1)*(3*i^2+3*i-1)/30)
%p A368348     end:
%p A368348 a:= n-> `if`(irem(n, 4)>1, 0, b(n^4, n)):
%p A368348 seq(a(n), n=0..43);  # _Alois P. Heinz_, Jan 25 2024
%t A368348 b[n_, i_] := b[n, i] = Function[m, If[n > m, 0, If[n == m, 1, b[Abs[n-i^4], i-1] + b[n+i^4, i-1]]]][i*(i+1)*(2*i+1)*(3*i^2+3*i-1)/30];
%t A368348 a[n_] := If[Mod[n, 4] > 1, 0, b[n^4, n]];
%t A368348 Table[a[n], {n, 0, 55}] (* _Jean-François Alcover_, Feb 14 2025, after _Alois P. Heinz_ *)
%Y A368348 Cf. A000583, A063890, A158465, A368243, A368845.
%K A368348 nonn
%O A368348 0,18
%A A368348 _Ilya Gutkovskiy_, Jan 25 2024
%E A368348 a(46)-a(59) from _Alois P. Heinz_, Jan 25 2024