A232988 Numerators of coefficients in q-expansion of Sum_{n = -oo,oo, n != 0} (((-1)^(n-1)/(2*n^2))*(sin(n*Pi/3)+sin(2*n*Pi/3))/(1-q^n))/sqrt(3), excluding the constant term.

0, 1, 1, 1, 1, 24, 1, 50, 1, 1, 24, 120, 1, 170, 50, 24, 1, 288, 1, 362, 24, 50, 120, 528, 1, 601, 170, 1, 50, 840, 24, 962, 1, 120, 288, 48, 1, 1370, 362, 170, 24, 1680, 50, 1850, 120, 24, 528, 2208, 1, 2451, 601, 288, 170, 2808, 1, 576, 50, 362, 840, 3480, 24, 3722, 962, 50, 1, 816, 120, 4490, 288, 528, 48

Offset

0,6

Links

Table of n, a(n) for n=0..70.

S. Bloch, P. Vanhove, The elliptic dilogarithm for the sunset graph, arXiv preprint arXiv:1309.5865, 2013 (see Eq. (1.1)).

Example

q+q^2+q^3+q^4+(24/25)*q^5+q^6+(50/49)*q^7+q^8+q^9+(24/25)*q^10+(120/121)*q^11+q^12+(170/169)*q^13+...

Maple

M:=100;
t1:=add( ((-1)^(n-1)/(2*n^2))*(sin(n*Pi/3)+sin(2*n*Pi/3))/(1-q^n), n=1..M)
+  add( ((-1)^(n-1)/(2*n^2))*(sin(n*Pi/3)+sin(2*n*Pi/3))/(1-q^n), n=-M..-1);
t2:=series(t1, q, M);
t3:=series((t2-coeff(t2, q, 0))/sqrt(3), q, M);
t4:=seriestolist(t3);
t5:=map(numer, t4); # A232988
t6:=map(denom, t4); # A232989

Crossrefs

Cf. A232989 (denominators).

Sequence in context: A280631 A040599 A076721 * A292781 A090215 A318105

Adjacent sequences: A232985 A232986 A232987 * A232989 A232990 A232991

Keyword

nonn,frac

Author

N. J. A. Sloane, Dec 09 2013

Status

approved