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 A010831 Expansion of Product_{k>=1} (1-x^k)^26. 2
 1, -26, 299, -1950, 7475, -13754, -12220, 132756, -276575, 0, 1010100, -1486030, -519961, 2486300, 829725, -2215486, -11643060, 18523050, 16317925, -42861650, 0, 11010090, 59644221, -5743400, -138219900 (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. S. R. Finch, Powers of Euler's q-Series, arXiv:math/0701251 [math.NT], 2007. Index entries for expansions of Product_{k >= 1} (1-x^k)^m FORMULA a(0) = 1, a(n) = -(26/n) * Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Aug 13 2023 EXAMPLE 1 - 26*x + 299*x^2 - 1950*x^3 + 7475*x^4 - 13754*x^5 - 12220*x^6 + 132756*x^7 + ... MATHEMATICA CoefficientList[Expand@ Product[(1 - x^k)^26, {k, 25}], x, 25] (* Michael De Vlieger, Jun 08 2016 *) CROSSREFS Column k=26 of A286354. Cf. A000203, A126581, A322433. Sequence in context: A224331 A125414 A208600 * A022718 A014472 A000498 Adjacent sequences: A010828 A010829 A010830 * A010832 A010833 A010834 KEYWORD sign AUTHOR N. J. A. Sloane STATUS approved

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Last modified August 12 04:50 EDT 2024. Contains 375085 sequences. (Running on oeis4.)