login
This site is supported by donations to The OEIS 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!)
A173519 Number of partitions of n*(n+1)/2 into parts not greater than n. 10
1, 1, 2, 7, 23, 84, 331, 1367, 5812, 25331, 112804, 511045, 2348042, 10919414, 51313463, 243332340, 1163105227, 5598774334, 27119990519, 132107355553, 646793104859, 3181256110699, 15712610146876, 77903855239751, 387609232487489, 1934788962992123 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) is also the number of partitions of n^3 into n distinct parts <= n*(n+1).  a(3) = 7: [4,11,12], [5,10,12], [6,9,12], [6,10,11], [7,8,12], [7,9,11], [8,9,10]. - Alois P. Heinz, Jan 25 2012

LINKS

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..720 (terms 0..200 from Alois P. Heinz)

FORMULA

a(n) = A026820(A000217(n),n).

a(n) ~ c * d^n / n^2, where d = 5.4008719041181541524660911191042700520294... = A258234, c = 0.6326058791290010900659134913629203727... . - Vaclav Kotesovec, Sep 07 2014

MATHEMATICA

Table[Length[IntegerPartitions[n(n + 1)/2, n]], {n, 10}] (* Alonso del Arte, Aug 12 2011 *)

Table[SeriesCoefficient[Product[1/(1-x^k), {k, 1, n}], {x, 0, n*(n+1)/2}], {n, 0, 20}] (* Vaclav Kotesovec, May 25 2015 *)

PROG

(PARI)

a(n)=

{

    local(tr=n*(n+1)/2, x='x+O('x^(tr+3)), gf);

    gf = 1 / prod(k=1, n, 1-x^k); /* g.f. for partitions into parts <=n */

    return( polcoeff( truncate(gf), tr ) );

} /* Joerg Arndt, Aug 14 2011 */

CROSSREFS

Cf. A066655, A097356, A258234.

Sequence in context: A150334 A150335 A150336 * A151292 A179533 A150337

Adjacent sequences:  A173516 A173517 A173518 * A173520 A173521 A173522

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Feb 20 2010

EXTENSIONS

More terms from D. S. McNeil, Aug 12 2011

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 18 20:57 EST 2019. Contains 319282 sequences. (Running on oeis4.)