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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 (list; graph; refs; listen; history; text; internal format)
 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 - Michael Somos, Nov 04 2015 REFERENCES Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 3, 2nd equation.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 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. Cf. A053270, A257640. Sequence in context: A019459 A276024 A274233 * A236914 A152902 A027084 Adjacent sequences:  A256206 A256207 A256208 * A256210 A256211 A256212 KEYWORD nonn AUTHOR N. J. A. Sloane, Mar 25 2015 STATUS approved

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Last modified October 20 17:50 EDT 2019. Contains 328268 sequences. (Running on oeis4.)