login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A022728 Expansion of Product_{m>=1} (1-m*q^m)^-4. 2
1, 4, 18, 64, 219, 676, 2030, 5736, 15793, 41864, 108430, 273240, 675526, 1634780, 3891960, 9108872, 21018870, 47815572, 107446898, 238524144, 523812125, 1138233100, 2449710880, 5223395480, 11042278208 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 4, g(n) = n. - Seiichi Manyama, Dec 29 2017

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: exp(4*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018

MATHEMATICA

With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^-4, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Jul 25 2018 *)

PROG

(PARI) m=50; q='q+O('q^m); Vec(prod(n=1, m, (1-n*q^n)^-4)) \\ G. C. Greubel, Jul 25 2018

(MAGMA) n:=50; R<x>:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^4:m in [1..n]])); // G. C. Greubel, Jul 25 2018

CROSSREFS

Column k=4 of A297328.

Sequence in context: A100177 A083321 A255611 * A231950 A246134 A115112

Adjacent sequences:  A022725 A022726 A022727 * A022729 A022730 A022731

KEYWORD

nonn

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 September 20 01:58 EDT 2019. Contains 327207 sequences. (Running on oeis4.)