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%I #20 Jan 11 2024 08:20:07
%S 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,
%T 56,1,51,46,17,16,130,1,19,67,139,1,105,1,142,162,23,1,315,2,151,121,
%U 246,1,219,211,321,154,29,1,1021,1,31,219,488,496,495,1,594,232,834,1,1439,1
%N Number of compositions of n such that every part is divisible by number of parts.
%H Alois P. Heinz, <a href="/A143862/b143862.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: Sum_{k>=0} x^(k^2) / (1 - x^k)^k.
%F G.f.: 1 + Sum_{n>=1} (1 + x^n)^(n-1) * x^n. - _Paul D. Hanna_, Jul 09 2019
%F a(n) = Sum_{d|n} binomial(n/d-1, d-1) for n>0 with a(0) = 1. - _Paul D. Hanna_, Apr 25 2018
%F G.f.: 1 + Sum_{n>=1} (x^n/(1-x^n))^n (conjecture). - _Joerg Arndt_, Jan 04 2024
%o (PARI) {a(n) = if(n==0,1, sumdiv(n,d, binomial(n/d-1,d-1) ))}
%o for(n=0,50, print1(a(n),", ")) \\ _Paul D. Hanna_, Apr 25 2018
%Y Cf. A143773, A261605.
%K easy,nonn
%O 0,5
%A _Vladeta Jovovic_, Sep 03 2008
%E More terms from _Franklin T. Adams-Watters_, Apr 09 2009