A369517 a(n) = [x^(n^4)] Product_{k=1..n} (x^(k^4) + 1 + 1/x^(k^4)).
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 9, 20, 43, 85, 183, 394, 1010, 2254, 5589, 12383, 31226, 71153, 182382, 426055, 1105686, 2615167, 6906858, 16607500, 44276140, 107836782, 290059089, 715361182, 1937639649, 4829754357, 13160903826, 33112002835, 90800047879
Offset: 0
Keywords
Programs
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Maple
b:= proc(n, i) option remember; (m-> `if`(n>m, 0, `if`(n=m, 1, b(n, i-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-> b(n^4, n): seq(a(n), n=0..33); # Alois P. Heinz, Jan 25 2024 -
Mathematica
b[n_, i_] := b[n, i] = Function[m, If[n > m, 0, If[n == m, 1, b[n, i-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_] := b[n^4, n]; Table[a[n], {n, 0, 37}] (* Jean-François Alcover, Feb 14 2025, after Alois P. Heinz *)
Extensions
a(34)-a(37) from Alois P. Heinz, Jan 25 2024