cp's OEIS Frontend

A226541 Number of unimodal compositions of n where the maximal part appears three times.

%I A226541 #30 Oct 24 2018 16:24:35
%S A226541 1,0,0,1,0,0,1,2,3,5,7,11,16,24,34,51,71,102,143,201,276,384,522,714,
%T A226541 964,1301,1739,2328,3084,4085,5377,7064,9226,12036,15616,20228,26092,
%U A226541 33584,43067,55125,70308,89502,113598,143889,181755,229160,288186,361750,453046,566346,706464
%N A226541 Number of unimodal compositions of n where the maximal part appears three times.
%H A226541 Alois P. Heinz, <a href="/A226541/b226541.txt">Table of n, a(n) for n = 0..10000</a>
%F A226541 G.f.: sum(n>=0, x^(3*n) / prod(k=1..n-1, 1-x^k )^2 ); replace 3 by m to obtain g.f. for "... max part appears m times".
%F A226541 a(n) ~ Pi^2 * exp(2*Pi*sqrt(n/3)) / (16 * 3^(7/4) * n^(9/4)). - _Vaclav Kotesovec_, Oct 24 2018
%o A226541 (PARI) N=66; x='x+O('x^N); Vec(sum(n=0,N, x^(3*n) / prod(k=1,n-1, 1-x^k )^2 ))
%Y A226541 Cf. A006330 (max part appears once), A114921 (max part appears twice).
%Y A226541 Cf. A188674 (max part m appears m times), A001522 (max part m appears at least m times).
%Y A226541 Cf. A001523 (max part appears any number of times).
%Y A226541 Cf. A000009 (symmetric, max part m appears once; also symmetric, max part appears an odd number of times).
%Y A226541 Cf. A035363 (symmetric, max part m appears twice; also symmetric, max part appears an even number of times).
%Y A226541 Cf. A087897 (symmetric, max part m appears 3 times).
%Y A226541 Cf. A027349 (symmetric, max part m appears m times), A189357 (symmetric, max part m appears at least m times).
%Y A226541 Column k=3 of A247255.
%K A226541 nonn
%O A226541 0,8
%A A226541 _Joerg Arndt_, Jun 10 2013