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!)
A320755 Number of partitions of n with nine kinds of 1. 2
1, 9, 46, 175, 551, 1517, 3775, 8677, 18703, 38223, 74682, 140403, 255280, 450734, 775440, 1303509, 2146040, 3467254, 5506807, 8610369, 13271183, 20186110, 30330668, 45058828, 66234905, 96406840, 139032605, 198774473, 281879613, 396670035, 554170514, 768909964 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

FORMULA

G.f.: 1/(1-x)^9 * 1/Product_{j>1} (1-x^j).

Euler transform of 9,1,1,1,... .

a(n) ~ 4 * 3^(7/2) * n^3 * exp(Pi*sqrt(2*n/3)) / Pi^8. - Vaclav Kotesovec, Oct 24 2018

MAPLE

a:= proc(n) option remember; `if`(n=0, 1, add(

      (numtheory[sigma](j)+8)*a(n-j), j=1..n)/n)

    end:

seq(a(n), n=0..40);

MATHEMATICA

nmax = 50; CoefficientList[Series[1/((1-x)^8 * Product[1-x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 24 2018 *)

PROG

(PARI) x='x+O('x^30); Vec(1/((1-x)^9*prod(j=2, 40, 1-x^j))) \\ G. C. Greubel, Oct 27 2018

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)^9*(&*[1-x^j: j in [2..30]])))); // G. C. Greubel, Oct 27 2018

CROSSREFS

Column k=9 of A292508.

Sequence in context: A260513 A001781 A258477 * A053308 A201458 A034487

Adjacent sequences:  A320752 A320753 A320754 * A320756 A320757 A320758

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 20 2018

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 26 13:34 EDT 2021. Contains 347668 sequences. (Running on oeis4.)