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

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A023880 Number of partitions in expanding space. 9
1, 1, 5, 32, 298, 3531, 51609, 894834, 17980052, 410817517, 10518031721, 298207687029, 9273094072138, 313757506696967, 11474218056441581, 450961669608632160, 18954582520550896213, 848384721904740036422, 40285256621556957160307, 2022695276960566890383148 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also partitions of n into 1 sort of 1, 4 sorts of 2, 27 sorts of 3, ..., k^k sorts of k. - Joerg Arndt, Feb 04 2015

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

FORMULA

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

a(n) ~ n^n * (1 + exp(-1)/n + (exp(-1)/2 + 5*exp(-2))/n^2). - Vaclav Kotesovec, Mar 14 2015

a(n) = (1/n)*Sum_{k=1..n} A283498(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 11 2017

MAPLE

with(numtheory):

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

      add(d*d^d, d=divisors(j)) *a(n-j), j=1..n)/n)

    end:

seq(a(n), n=0..30);  # Alois P. Heinz, Feb 04 2015

MATHEMATICA

nmax=20; CoefficientList[Series[Product[1/(1-x^k)^(k^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 14 2015 *)

PROG

(PARI) m=30; x='x+O('x^m); Vec(prod(k=1, m, 1/(1-x^k)^(k^k))) \\ G. C. Greubel, Oct 31 2018

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-x^k)^(k^k): k in [1..m]]) )); // G. C. Greubel, Oct 31 2018

CROSSREFS

Sequence in context: A305305 A331339 A307497 * A104031 A294957 A023882

Adjacent sequences:  A023877 A023878 A023879 * A023881 A023882 A023883

KEYWORD

nonn

AUTHOR

Olivier Gérard

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 January 17 15:12 EST 2020. Contains 330958 sequences. (Running on oeis4.)