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

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, 0, 0, 4080, 9309, 0, 0, 44775, 72659, 0, 0, 430297, 781505, 0, 0, 3934457, 7765047, 0, 0, 44740433, 78818429, 0, 0, 463089552, 900950811, 0, 0, 5344766190, 9806206864, 0, 0

Offset: 0

Author

Ilya Gutkovskiy, Jan 25 2024

Keywords

• nonn

Crossrefs

Cf. A000583, A063890, A158465, A368243, A368845.

Programs

Maple

b:= proc(n, i) option remember; (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)
    end:
a:= n-> `if`(irem(n, 4)>1, 0, b(n^4, n)):
seq(a(n), n=0..43);  # Alois P. Heinz, Jan 25 2024

Mathematica

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];
a[n_] := If[Mod[n, 4] > 1, 0, b[n^4, n]];
Table[a[n], {n, 0, 55}] (* Jean-François Alcover, Feb 14 2025, after Alois P. Heinz *)

Extensions

a(46)-a(59) from Alois P. Heinz, Jan 25 2024