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 A010839 Expansion of Product_{k >= 1} (1-x^k)^48. 2
 1, -48, 1080, -15040, 143820, -985824, 4857920, -16295040, 28412910, 38671600, -424520544, 1268350272, -1211937160, -4306546080, 18293091840, -23522231424, -26299018683, 137218594320, -150999182320, -134713340160 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES Morris Newman, A table of the coefficients of the powers of eta(tau), Nederl. Akad. Wetensch. Proc. Ser. A. 59 = Indag. Math. 18 (1956), 204-216. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 M. Boylan, Exceptional congruences for the coefficients of certain eta-product newforms, J. Number Theory 98 (2003), no. 2, 377-389. Index entries for expansions of Product_{k >= 1} (1-x^k)^m FORMULA Let b(q) be the determinant of the 3 X 3 Hankel matrix [E_4, E_6, E_8 ; E_6, E_8, E_10 ; E_8, E_10, E_12]. G.f. is -691*b(q)/(q^2*1728^2*250). - Seiichi Manyama, Jul 17 2017 a(n) = (A290010(n+2) - A290009(n+2) + 691*(A282330(n+2) - A282332(n+2)))/(1728^2*250). - Seiichi Manyama, Jul 19 2017 a(0) = 1, a(n) = -(48/n) * Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Aug 13 2023 EXAMPLE 1 - 48*x + 1080*x^2 - 15040*x^3 + 143820*x^4 - 985824*x^5 + 4857920*x^6 - 16295040*x^7 + ... CROSSREFS Column k=48 of A286354. Cf. A000203, A082558, A126581, A282330 (E_8^3), A282332 (E_6*E_8*E_10 = E4*E_10^2), A290009, A290010. Sequence in context: A272778 A160068 A229387 * A000156 A319309 A022077 Adjacent sequences: A010836 A010837 A010838 * A010840 A010841 A010842 KEYWORD sign AUTHOR N. J. A. Sloane STATUS approved

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Last modified November 30 18:31 EST 2023. Contains 367461 sequences. (Running on oeis4.)