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

1, 0, 0, 1, 0, 0, 1, 2, 3, 5, 7, 11, 16, 24, 34, 51, 71, 102, 143, 201, 276, 384, 522, 714, 964, 1301, 1739, 2328, 3084, 4085, 5377, 7064, 9226, 12036, 15616, 20228, 26092, 33584, 43067, 55125, 70308, 89502, 113598, 143889, 181755, 229160, 288186, 361750, 453046, 566346, 706464

Offset: 0

Author

Joerg Arndt, Jun 10 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A006330 (max part appears once), A114921 (max part appears twice).

Cf. A188674 (max part m appears m times), A001522 (max part m appears at least m times).

Cf. A001523 (max part appears any number of times).

Cf. A000009 (symmetric, max part m appears once; also symmetric, max part appears an odd number of times).

Cf. A035363 (symmetric, max part m appears twice; also symmetric, max part appears an even number of times).

Cf. A087897 (symmetric, max part m appears 3 times).

Cf. A027349 (symmetric, max part m appears m times), A189357 (symmetric, max part m appears at least m times).

Column k=3 of A247255.

Programs

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 ))

Formula

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".

a(n) ~ Pi^2 * exp(2*Pi*sqrt(n/3)) / (16 * 3^(7/4) * n^(9/4)). - Vaclav Kotesovec, Oct 24 2018