A143862 Number of compositions of n such that every part is divisible by number of parts.

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

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

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

For prime p, a(p) = 1, a(2*p) = p and a(p^2) = 2. - Peter Bala, Mar 02 2025

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

Cf. A143773, A261605.

Sequence in context: A113308 A325332 A358195 * A115118 A115121 A323523

Adjacent sequences: A143859 A143860 A143861 * A143863 A143864 A143865

Keyword

easy,nonn,changed

Author

Vladeta Jovovic, Sep 03 2008

Extensions

More terms from Franklin T. Adams-Watters, Apr 09 2009

Status

approved