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A256209
Coefficients of mock modular form H_2^(4) (divided by 16).
5
1, 3, 7, 14, 27, 49, 84, 141, 230, 364, 567, 867, 1302, 1932, 2829, 4091, 5859, 8309, 11675, 16275, 22513, 30914, 42174, 57176, 77049, 103263, 137669, 182616, 241110, 316910, 414750, 540603, 701903, 907928, 1170261, 1503238, 1924607, 2456349
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Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 3, 2nd equation.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
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
2 * a(n) = A053270(3*n) - A257640(3*n). - 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
Equals A256052/8.
Sequence in context: A276024 A274233 A369576 * A236914 A152902 A027084
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 25 2015
STATUS
approved