A283499 - OEIS

%I #15 Mar 12 2017 12:56:22

%S 1,-1,-4,-23,-223,-2767,-42268,-759008,-15672223,-365639304,

%T -9512549191,-273072804420,-8575012101043,-292422232720311,

%U -10762617713743350,-425245537127322111,-17953822507629389009,-806668679245000383731

%N Expansion of exp( Sum_{n>=1} -A283498(n)/n*x^n ) in powers of x.

%H Seiichi Manyama, <a href="/A283499/b283499.txt">Table of n, a(n) for n = 0..386</a>

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

%F a(n) = -(1/n)*Sum_{k=1..n} A283498(k)*a(n-k) for n > 0.

%t A[n_] :=  Sum[d^(d+ 1), {d, Divisors[n]}]; a[n_] := If[n==0, 1, -(1/n)*Sum[A[k]*a[n - k], {k, n}]]; Table[a[n], {n, 0, 17}] (* _Indranil Ghosh_, Mar 11 2017 *)

%o (PARI) a(n) = if(n==0, 1, -(1/n)*sum(k=1, n, sumdiv(k, d, d^(d + 1))*a(n - k)));

%o for(n=0, 20, print1(a(n), ", ")) \\ _Indranil Ghosh_, Mar 11 2017

%Y Cf. A023880, A283498.

%K sign

%O 0,3

%A _Seiichi Manyama_, Mar 09 2017