A283271 - OEIS

%I #15 Mar 05 2017 02:51:19

%S 1,-1,-16,-65,-55,807,4809,13135,550,-169070,-862710,-2281174,

%T -1221309,20194565,114391575,346400092,486546751,-1239516671,

%U -11089537215,-41702958960,-93143227027,-45337210750,674845109986,3682196642725,11405949184465,20796945542222

%N Expansion of exp( Sum_{n>=1} -sigma_5(n)*x^n/n ) in powers of x.

%H Seiichi Manyama, <a href="/A283271/b283271.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: Product_{n>=1} (1 - x^n)^(n^4).

%F a(n) = -(1/n)*Sum_{k=1..n} sigma_5(k)*a(n-k).

%Y Column k=4 of A283272.

%Y Cf. A023873 (exp( Sum_{n>=1} sigma_5(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), this sequence (k=5).

%K sign

%O 0,3

%A _Seiichi Manyama_, Mar 04 2017