login
A143862
Number of compositions of n such that every part is divisible by number of parts.
11
1, 1, 1, 1, 2, 1, 3, 1, 4, 2, 5, 1, 9, 1, 7, 7, 9, 1, 19, 1, 14, 16, 11, 1, 43, 2, 13, 29, 34, 1, 56, 1, 51, 46, 17, 16, 130, 1, 19, 67, 139, 1, 105, 1, 142, 162, 23, 1, 315, 2, 151, 121, 246, 1, 219, 211, 321, 154, 29, 1, 1021, 1, 31, 219, 488, 496, 495, 1, 594, 232, 834, 1, 1439, 1
OFFSET
0,5
LINKS
FORMULA
G.f.: Sum_{k>=0} x^(k^2) / (1 - x^k)^k.
G.f.: 1 + Sum_{n>=1} (1 + x^n)^(n-1) * x^n. - Paul D. Hanna, Jul 09 2019
a(n) = Sum_{d|n} binomial(n/d-1, d-1) for n>0 with a(0) = 1. - Paul D. Hanna, Apr 25 2018
G.f.: 1 + Sum_{n>=1} (x^n/(1-x^n))^n (conjecture). - Joerg Arndt, Jan 04 2024
PROG
(PARI) {a(n) = if(n==0, 1, sumdiv(n, d, binomial(n/d-1, d-1) ))}
for(n=0, 50, print1(a(n), ", ")) \\ Paul D. Hanna, Apr 25 2018
CROSSREFS
Sequence in context: A113308 A325332 A358195 * A115118 A115121 A323523
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Sep 03 2008
EXTENSIONS
More terms from Franklin T. Adams-Watters, Apr 09 2009
STATUS
approved