A321190 - OEIS

%I #6 Oct 29 2018 18:25:57

%S 1,1,6,47,778,25476,1752936,242632397,70015221566,41446777283255,

%T 49999934258165654,125272856707074638221,641938223803783115191706,

%U 6731818441446626626586172740,146378489075644780343627471981694,6505906463580477520696075719916583118

%N a(n) = [x^n] 1/(1 - Sum_{k>=1} k^n*x^k/(1 - x^k)).

%F a(n) = [x^n] 1/(1 - Sum_{k>=1} sigma_n(k)*x^k).

%F a(n) = [x^n] 1/(1 - Sum_{i>=1, j>=1} j^n*x^(i*j)).

%F a(n) = [x^n] 1/(1 + x * (d/dx) log(Product_{k>=1} (1 - x^k)^(k^(n-1)))).

%p seq(coeff(series((1-add(k^n*x^k/(1-x^k),k=1..n))^(-1),x,n+1), x, n), n = 0 .. 25); # _Muniru A Asiru_, Oct 29 2018

%t Table[SeriesCoefficient[1/(1 - Sum[k^n x^k/(1 - x^k), {k, 1, n}]), {x, 0, n}], {n, 0, 15}]

%t Table[SeriesCoefficient[1/(1 - Sum[DivisorSigma[n, k] x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 15}]

%t Table[SeriesCoefficient[1/(1 - Sum[Sum[j^n x^(i j), {j, 1, n}], {i, 1, n}]), {x, 0, n}], {n, 0, 15}]

%Y Cf. A023887, A129921, A180305, A319647, A320649, A321042.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Oct 29 2018