A294626 - OEIS

%I #20 Jun 03 2018 09:28:53

%S 42,-3171,515242,-88552695,16361485098,-3146078130083,622295456184618,

%T -125653124401054383,25774485201611434666,-5353054527354475135971,

%U 1122995842490069166600618,-237552033781060445940477047,50601782105864798623718932266

%N a(n) = (1/(24*n)) * Sum_{d|n} A008683(n/d) * (A288877(d) - A288261(d)).

%H Seiichi Manyama, <a href="/A294626/b294626.txt">Table of n, a(n) for n = 1..424</a>

%F a(n) ~ -(-1)^n * exp(Pi*sqrt(3)*n) / (8*n). - _Vaclav Kotesovec_, Jun 03 2018

%t terms = 13;

%t E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];

%t E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];

%t E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];

%t a[n_] := (1/(24 n))*Sum[MoebiusMu[n/d]*SeriesCoefficient[E4[x]/E2[x] - E6[x]/E4[x], {x, 0, d}], {d, Divisors[n]}];

%t Array[a, terms] (* _Jean-François Alcover_, Feb 26 2018 *)

%Y Cf. A008683, A288261, A288877, A294974.

%K sign

%O 1,1

%A _Seiichi Manyama_, Feb 12 2018