A000739 Expansion of Product_{k>=1} (1 - x^k)^16.

1, -16, 104, -320, 260, 1248, -3712, 1664, 6890, -7280, -5568, -4160, 33176, 4640, -74240, 29824, 14035, 54288, 27040, -142720, 1508, -110240, 289536, 222720, -380770, -83200, -123904, 142912, 7640, 408000, 386048

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy

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.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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

a(0) = 1, a(n) = -(16/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

G.f.: exp(-16*Sum_{k>=1} x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 05 2018