OFFSET
0,1
COMMENTS
Coefficients of 3-point function in dimension 3 [Morrison].
LINKS
Gheorghe Coserea, Table of n, a(n) for n = 0..300
P. Candelas et al., A pair of Calabi-yau manifolds as an exactly soluble superconformal theory, Nuclear Phys. B 359 (1991), 21-74.
Daniel B. Grunberg and Pieter Moree, with an Appendix by Don Zagier, Sequences of enumerative geometry: congruences and asymptotics, arXiv:math/0610286 [math.NT], 2006.
David R. Morrison, Mathematical Aspects of Mirror Symmetry, arXiv:alg-geom/9609021, 1996, see Table 1 p. 60; in Complex Algebraic Geometry (J. Kollár, ed.), IAS/Park City Math. Series, vol. 3, 1997, pp. 265-340.
FORMULA
Sum_{n >= 0} a(n)*q^n = 5 + Sum_{n >= 1} A060041(n)*n^3*q^n/(1-q^n).
EXAMPLE
PROG
(PARI) cumsum(v) = for(i=2, #v, v[i] += v[i-1]); v;
seq(N, {d=5}) = {
my(x = 'x + O('x^(N+1)), h = cumsum(vector(d*N, n, 1/n)),
y0 = sum(n=0, N, (d*n)!/n!^d * x^n),
y1 = d * sum(n = 1, N, ((d*n)!/n!^d * (h[d*n] - h[n])) * x^n),
Qx = x * exp(y1/y0), Xq = serreverse(Qx));
Vec(d * (x * Xq'/Xq)^(d-2) / ((1 - d^d*Xq) * sqr(subst(y0, 'x, Xq))));
};
seq(20) \\ Gheorghe Coserea, Jul 29 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 30 2001
EXTENSIONS
More terms from Vladeta Jovovic, Apr 01 2001
a(6) corrected and a(10)-a(12) added by Gheorghe Coserea, Jul 28 2016
STATUS
approved