A307241 - OEIS

%I #6 Mar 30 2019 08:39:18

%S 1,2,2,3,6,12,23,42,75,135,248,460,849,1554,2837,5192,9527,17490,

%T 32083,58809,107781,197578,362280,664320,1218069,2233202,4094289,

%U 7506602,13763219,25234674,46266927,84828138,155528132,285154061,522819002,958568628,1757496665,3222295912

%N a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k+1)*d(k+1)*a(n-k), where d() is the number of divisors (A000005).

%F G.f.: -x / Sum_{k>=1} (-x)^k/(1 - (-x)^k).

%F G.f.: 1 / (d/dx) log(Product_{k>=1} (1 - (-x)^k)^(1/k)).

%t a[0] = 1; a[n_] := a[n] = Sum[(-1)^(k + 1) DivisorSigma[0, k + 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 37}]

%t nmax = 37; CoefficientList[Series[-x/Sum[(-x)^k/(1 - (-x)^k), {k, 1, nmax + 1}], {x, 0, nmax}], x]

%t nmax = 37; CoefficientList[Series[1/D[Log[Product[(1 - (-x)^k)^(1/k), {k, 1, nmax + 1}]], x], {x, 0, nmax}], x]

%Y Cf. A000005, A002039, A129921, A307242.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Mar 30 2019