A320318 Number of weakly unimodal compositions of n in which the greatest part occurs exactly seven times.

1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 9, 11, 15, 19, 26, 33, 44, 56, 73, 92, 119, 149, 190, 238, 301, 375, 472, 586, 733, 908, 1129, 1394, 1727, 2124, 2619, 3213, 3946, 4824, 5904, 7196, 8776, 10667, 12965, 15714, 19045, 23019, 27816

Offset

0,16

Links

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

Wikipedia, Unimodality, Unimodal function

Formula

G.f.: Sum_{n>=0} x^(7*n) / Product_{j=1..n-1} (1-x^j)^2.

a(n) ~ Pi^6 * 6! * exp(2*Pi*sqrt(n/3)) / (2^9 * 3^(15/4) * n^(17/4)). - Vaclav Kotesovec, Oct 24 2018

Maple

b:= proc(n, i) option remember; `if`(i>n, 0,
      `if`(7*i=n, 1, 0)+add(b(n-i*j, i+1)*(j+1), j=0..n/i))
    end:
a:= n-> `if`(n=0, 1, b(n, 1)):
seq(a(n), n=0..70);

Crossrefs

Column k=7 of A247255.

Sequence in context: A283364 A131617 A214321 * A005577 A263362 A336733

Adjacent sequences: A320315 A320316 A320317 * A320319 A320320 A320321

Keyword

nonn

Author

Alois P. Heinz, Oct 10 2018

Status

approved