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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A023004 Number of partitions of n into parts of 5 kinds. 3
1, 5, 20, 65, 190, 506, 1265, 2990, 6765, 14725, 31027, 63505, 126730, 247170, 472295, 885723, 1633000, 2963840, 5302075, 9358470, 16313440, 28107365, 47902010, 80803485, 134992865, 223474667, 366772720, 597049255, 964375855, 1546208695, 2461649861, 3892774130 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is Euler transform of A010716. - Alois P. Heinz, Oct 17 2008

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Roland Bacher, P. De La Harpe, Conjugacy growth series of some infinitely generated groups. 2016. hal-01285685v2;

P. Nataf, M. Lajkó, A. Wietek, K. Penc, F. Mila, A. M. Läuchli, Chiral spin liquids in triangular lattice SU (N) fermionic Mott insulators with artificial gauge fields, arXiv preprint arXiv:1601.00958 [cond-mat.quant-gas], 2016.

N. J. A. Sloane, Transforms

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

FORMULA

G.f.: Product_{m>=1} 1/(1-x^m)^5.

a(n) ~ 5^(3/2) * exp(Pi * sqrt(10*n/3)) / (32 * 3^(3/2) * n^2) * (1 - (3*sqrt(6/5) /Pi + 5*sqrt(5/6)*Pi/24) / sqrt(n)). - Vaclav Kotesovec, Feb 28 2015, extended Jan 16 2017

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

MAPLE

with(numtheory): a:=proc(n) option remember; `if`(n=0, 1, add(add(d*5, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # Alois P. Heinz, Oct 17 2008

MATHEMATICA

nmax=50; CoefficientList[Series[Product[1/(1-x^k)^5, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 28 2015 *)

PROG

(PARI) \ps100 for(n=0, 100, print1((polcoeff(1/eta(x)^5, n, x)), ", "))

CROSSREFS

Cf. 5th column of A144064. - Alois P. Heinz, Oct 17 2008

Sequence in context: A160506 A277212 A160528 * A001873 A120297 A271066

Adjacent sequences:  A023001 A023002 A023003 * A023005 A023006 A023007

KEYWORD

nonn

AUTHOR

David W. Wilson

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified April 30 08:33 EDT 2017. Contains 285645 sequences.