OFFSET
0,2
COMMENTS
The coefficients occur on page 94, Table 24, column 1A for McKay-Thompson series H_{1A,2}^(4) in the Cheng et al. arXiv article. - Michael Somos, Nov 04 2015
REFERENCES
Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 3, 2nd equation.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
Miranda C. N. Cheng, John F. R. Duncan, Jeffrey A. Harvey, Umbral Moonshine, arXiv:1204.2779 [math.RT], 2012-2013.
FORMULA
G.f.: Sum_{k>0} x^(k-1) * (1 + x) * ... * (1 + x^(2*k-2)) / ((1 + x) * (1 + x^3) * ... (1 + x^(2*k-1)))^2. - Michael Somos, Nov 04 2015
EXAMPLE
G.f. = 1 + 3*x + 7*x^2 + 14*x^3 + 27*x^4 + 49*x^5 + 84*x^6 + 141*x^7 + ...
G.f. = q^3 + 3*q^7 + 7*q^11 + 14*q^15 + 27*q^19 + 49*q^23 + 84*q^27 + ...
MATHEMATICA
nmax = 50; a:= CoefficientList[Series[q*Sum[q^(k - 1)*(Product[1 + q^j, {j, 1, 2 k - 2}])/(Product[1 - q^(2 j - 1), {j, 1, k}])^2, {k, 0, nmax}], {q, 0, 150}], q]; Table[a[[n]], {n, 1, 100}] (* G. C. Greubel, Jul 27 2018 *)
PROG
(PARI) {a(n) = if( n<0, 0, n++; polcoeff( sum(k=1, n, x^k * prod(i=1, 2*k - 2, 1 + x^i, 1 + x * O(x^(n - k))) / prod(i=1, k, 1 - x^(2*i - 1), 1 + x * O(x^(n - k)))^2), n))}; /* Michael Somos, Nov 04 2015 */
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 25 2015
STATUS
approved