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%I #24 Jan 25 2024 20:09:31
%S 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 0,0,4080,9309,0,0,44775,72659,0,0,430297,781505,0,0,3934457,7765047,
%U 0,0,44740433,78818429,0,0,463089552,900950811,0,0,5344766190,9806206864,0,0
%N a(n) = [x^(n^4)] Product_{k=1..n} (x^(k^4) + 1/x^(k^4)).
%p b:= proc(n, i) option remember; (m-> `if`(n>m, 0, `if`(n=m, 1,
%p 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 end:
%p a:= n-> `if`(irem(n, 4)>1, 0, b(n^4, n)):
%p seq(a(n), n=0..43); # _Alois P. Heinz_, Jan 25 2024
%Y Cf. A000583, A063890, A158465, A368243, A368845.
%K nonn
%O 0,18
%A _Ilya Gutkovskiy_, Jan 25 2024
%E a(46)-a(59) from _Alois P. Heinz_, Jan 25 2024