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 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

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