A353947 Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} sigma(n)*x^n, where sigma = A000203.

1, 2, 1, -1, -3, -1, -1, -3, 3, -17, -1, -6, 3, -22, 1, -28, 1, -68, 7, -262, -13, -199, 27, -341, 29, -647, 3, -1431, -25, -476, -81, -4816, 89, -7384, 637, -17565, -275, -27043, -263, -107113, -453, -98469, -583, -208302, 8121, -371798, -6661, -743344, 3045, -1060666

Offset: 1

Author

Ilya Gutkovskiy, May 12 2022

Keywords

• sign

Crossrefs

Cf. A000203, A320780, A328776, A353924, A353945, A353948, A353949.

Programs

Mathematica

A[m_, n_] := A[m, n] = Which[m == 1, DivisorSigma[1, n], m > n >= 1, 0, True, A[m - 1, n] - A[m - 1, m - 1] A[m - 1, n - m + 1]]; a[n_] := A[n, n]; a /@ Range[1, 50]

Formula

Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} x^n / (1 - x^n)^2.