login
A365631
Number of partitions of n with exactly five part sizes.
6
1, 2, 5, 10, 20, 36, 58, 95, 147, 222, 323, 462, 636, 889, 1184, 1584, 2060, 2686, 3403, 4353, 5433, 6768, 8319, 10230, 12363, 15011, 17943, 21467, 25403, 30044, 35231, 41294, 48002, 55718, 64328, 74086, 84880, 97071, 110607, 125692, 142313, 160728, 181112, 203438, 228124
OFFSET
15,2
LINKS
FORMULA
G.f.: Sum_{0<i<j<k<l<m} x^(i+j+k+l+m)/( (1-x^i)*(1-x^j)*(1-x^k)*(1-x^l)*(1-x^m) ).
EXAMPLE
a(16) = 2 because we have 6+4+3+2+1, 5+4+3+2+1+1.
MAPLE
# Using function P from A365676:
A365631 := n -> P(n, 5, n): seq(A365631(n), n = 15..59); # Peter Luschny, Sep 15 2023
PROG
(Python)
from sympy.utilities.iterables import partitions
def A365631(n): return sum(1 for p in partitions(n) if len(p)==5) # Chai Wah Wu, Sep 14 2023
CROSSREFS
A diagonal of A060177.
Column k=5 of A116608.
Cf. A364809.
Sequence in context: A325719 A000710 A160461 * A117487 A263348 A328548
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 13 2023
STATUS
approved