A283336 - OEIS

%I #13 Mar 16 2017 22:46:52

%S 1,-1,-32,-211,-285,5179,44784,162062,-125122,-5187417,-32587255,

%T -95706881,122837972,3039216222,17745876032,52825817007,-24340390929,

%U -1256623249600,-7805634068163,-26364952524572,-20649978457115,368666542515083,2777231006764690

%N Expansion of exp( Sum_{n>=1} -sigma_6(n)*x^n/n ) in powers of x.

%H Seiichi Manyama, <a href="/A283336/b283336.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: Product_{n>=1} (1 - x^n)^(n^5).

%F a(n) = -(1/n)*Sum_{k=1..n} sigma_6(k)*a(n-k).

%t a[n_] := If[n<1, 1,-(1/n) * Sum[DivisorSigma[6, k] a[n - k], {k, n}]]; Table[a[n], {n, 0, 22}] (* _Indranil Ghosh_, Mar 16 2017 *)

%o (PARI) a(n) = if(n<1, 1, -(1/n) * sum(k=1, n, sigma(k, 6) * a(n - k)));

%o for(n=0, 22, print1(a(n), ", ")) \\ _Indranil Ghosh_, Mar 16 2017

%Y Column k=5 of A283272.

%Y Cf. A023874 (exp( Sum_{n>=1} sigma_6(n)*x^n/n )).

%Y Cf. exp( Sum_{n>=1} -sigma_k(n)*x^n/n ): A010815 (k=1), A073592 (k=2), A283263 (k=3), A283264 (k=4), A283271 (k=5), this sequence (k=6), A283337 (k=7), A283338 (k=8), A283339 (k=9), A283340 (k=10).

%K sign

%O 0,3

%A _Seiichi Manyama_, Mar 05 2017