login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000728 Expansion of Product_{n>=1} (1-x^n)^5.
(Formerly M3742 N1529)
6
1, -5, 5, 10, -15, -6, -5, 25, 15, -20, 9, -45, -5, 25, 20, 10, 15, 20, -50, -35, -30, 55, -50, 15, 80, 1, 50, -35, -45, -15, 5, -50, -25, -55, 85, 51, 50, 10, -40, 65, 10, -10, -115, 50, -115, -100, 85, 80, -30, 5, 20, 45, 70, 65, 45, -55, -100 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Newman, Morris; 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. MR1955423 (2003k:11071)

M. 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. [Annotated scanned copy]

Index entries for expansions of Product_{k >= 1} (1-x^k)^m

FORMULA

a(0) = 1, a(n) = -(5/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 26 2017

G.f.: exp(-5*Sum_{k>=1} x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 05 2018

MATHEMATICA

CoefficientList[QPochhammer[x]^5 + O[x]^60, x] (* Jean-Fran├žois Alcover, Feb 10 2016 *)

CROSSREFS

Cf. A258405.

Sequence in context: A285932 A109064 A138506 * A242895 A242129 A022088

Adjacent sequences:  A000725 A000726 A000727 * A000729 A000730 A000731

KEYWORD

sign

AUTHOR

N. J. A. Sloane.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 26 02:56 EDT 2020. Contains 334613 sequences. (Running on oeis4.)