A000739 Expansion of Product_{k>=1} (1 - x^k)^16. (Formerly M5006 N2155)

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

0,2

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.

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

Crossrefs

Sequence in context: A245872 A304505 A210687 * A186852 A010079 A022708

Adjacent sequences: A000736 A000737 A000738 * A000740 A000741 A000742

Keyword

sign,easy

Author

N. J. A. Sloane

Status

approved