A382980 a(n) = [(x*y)^n] Product_{k>=1} (1 + x^k - y^k).

1, 0, 0, 0, 0, 2, 0, 4, 2, 6, 4, 10, 6, 14, 10, 14, 10, 20, 6, 22, 2, 10, 14, 16, -32, 14, 6, -26, -20, 12, -56, 28, -2, -38, 96, 56, -38, 200, 298, 82, 338, 460, 446, 666, 852, 456, 1580, 1172, 1048, 1608, 2426, 1236, 2810, 2222, 2824, 2066, 3716, 1612, 5498

Offset: 0

Author

Seiichi Manyama, Apr 11 2025

Keywords

• sign

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..130

Crossrefs

Main diagonal of A382975.

Cf. A365662.

Programs

Magma

nmax := 60; prec := 2*nmax + 10; Rx := PowerSeriesRing(Rationals(), prec); Rxy := PowerSeriesRing(Rx, prec); P := Rxy!1; for k in [1..prec] do P *:= (1 + x^k - y^k); end for; seq := [Coefficient(Coefficient(P, n), n) : n in [0..nmax]]; print seq; // Vincenzo Librandi, Apr 13 2025

Mathematica

a[n_]:=SeriesCoefficient[Product[(1+x^k-y^k),{k,1,n}],{x,0,n},{y,0,n}];Table[a[n],{n,0,60}] (* Vincenzo Librandi, Apr 13 2025 *)