A353923 Product_{n>=1} (1 + a(n)*x^n) = 1 + Sum_{n>=1} tau(n)*x^n, where tau = A000005.

1, 2, 0, 3, -1, -1, -1, 9, 1, -7, 0, 4, -1, -19, 2, 94, -2, -57, 2, 81, -4, -186, 3, 226, 3, -632, -2, 1040, 1, -2060, -15, 10975, 17, -7720, -1, 13980, 9, -27595, -18, 50432, -10, -97582, 24, 191827, -17, -364695, 27, 580609, -37, -1338741, 45, 2658068, -11, -4909146, -98

Offset: 1

Author

Ilya Gutkovskiy, May 11 2022

Keywords

• sign

Crossrefs

Cf. A000005, A320779, A328775, A353924, A353925, A353926.

Programs

Mathematica

A[m_, n_] := A[m, n] = Which[m == 1, DivisorSigma[0, n], m > n >= 1, 0, True, A[m - 1, n] - A[m - 1, m - 1] A[m, n - m + 1]]; a[n_] := A[n, n]; a /@ Range[1, 55]

Formula

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