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A226541 Number of unimodal compositions of n where the maximal part appears three times. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

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

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

PROG

(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 ))

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.

Sequence in context: A308991 A326467 A326592 * A281578 A173199 A023435

Adjacent sequences:  A226538 A226539 A226540 * A226542 A226543 A226544

KEYWORD

nonn

AUTHOR

Joerg Arndt, Jun 10 2013

STATUS

approved

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Last modified February 26 18:29 EST 2020. Contains 332293 sequences. (Running on oeis4.)