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

 

Logo


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. 8
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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 22 04:15 EST 2018. Contains 299429 sequences. (Running on oeis4.)