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A320316 Number of weakly unimodal compositions of n in which the greatest part occurs exactly five times. 2
1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 3, 4, 5, 7, 9, 13, 17, 24, 32, 44, 58, 79, 103, 138, 180, 237, 307, 402, 517, 670, 859, 1104, 1407, 1799, 2280, 2896, 3656, 4616, 5801, 7291, 9120, 11407, 14215, 17701, 21971, 27252, 33699, 41637, 51314, 63170, 77590, 95202 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,12

LINKS

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

Wikipedia, Unimodality, Unimodal function

FORMULA

G.f.: Sum_{n>=0} x^(5*n) / Product_{j=1..n-1} (1-x^j)^2.

a(n) ~ Pi^4 * exp(2*Pi*sqrt(n/3)) / (16 * 3^(7/4) * n^(13/4)). - Vaclav Kotesovec, Oct 24 2018

MAPLE

b:= proc(n, i) option remember; `if`(i>n, 0,

      `if`(5*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=5 of A247255.

Sequence in context: A055167 A064628 A188674 * A236166 A017834 A286225

Adjacent sequences:  A320313 A320314 A320315 * A320317 A320318 A320319

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 10 2018

STATUS

approved

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Last modified January 16 00:05 EST 2021. Contains 340195 sequences. (Running on oeis4.)