OFFSET
0,3
COMMENTS
Also appears in Ramanujan's theory of elliptic functions, signature 6 (cf. A113424). Almkvist et al. give a real and complex Ansatz for the second-order, ordinary differential equation: T_R = 1 + x*{Z[[x]]}, T_C = T_R*log(x) + x*{Z[[x]]}.
REFERENCES
B.C. Berndt, "Ramanujan's Notebooks Part II", Springer, 2012, pages 80-82.
LINKS
G. Almkvist et al., Generalizations of Clausen's Formula and Algebraic Transformations of Calabi-Yau Differential Equations, Proceedings of the Edinburgh Mathematical Society, 54 (2011), p. 275.
MATHEMATICA
G[nMax_] := Dot[RecurrenceTable[{Dot[{(6*n - 11)^2 (6*n - 7)^2 (18*n - 5), -36 (n - 1) (385 - 2426*n + 4968*n^2 - 4248*n^3 + 1296*n^4), 1296 (n - 1) n^3 (18*n - 23)},
a[n - #] & /@ Reverse[Range[0, 2]]] == 0, a[0] == 0, a[1] == 13/18}, a, {n, 0, nMax}], x^Range[0, nMax]];
qSer[nMax_] := Expand[Times[x, Normal[ Series[Exp[Divide[G[nMax], Hypergeometric2F1[1/6, 5/6, 1, x]]], {x, 0, nMax}]]]];
CoefficientList[(1/k)*qSer[12] /. {x -> k*x}, x] /. {k -> 432}
CROSSREFS
KEYWORD
nonn
AUTHOR
Bradley Klee, Jun 27 2019
STATUS
approved