A353947 - OEIS

%I #6 May 13 2022 10:00:04

%S 1,2,1,-1,-3,-1,-1,-3,3,-17,-1,-6,3,-22,1,-28,1,-68,7,-262,-13,-199,

%T 27,-341,29,-647,3,-1431,-25,-476,-81,-4816,89,-7384,637,-17565,-275,

%U -27043,-263,-107113,-453,-98469,-583,-208302,8121,-371798,-6661,-743344,3045,-1060666

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

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

%t 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]

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

%K sign

%O 1,2

%A _Ilya Gutkovskiy_, May 12 2022