A171625 - OEIS

%I #15 Feb 24 2015 04:36:30

%S 1,1,3,7,15,29,58,118,242,493,997,2005,4024,8071,16183,32439,65003,

%T 130214,260768,522084,1045045,2091489,4185209,8373979,16753651,

%U 33516419,67047467,134118462,268274858,536611011,1073321222,2146803124,4293866550,8588154649

%N Number of compositions of n such that the number of parts is divisible by the smallest part.

%H Alois P. Heinz, <a href="/A171625/b171625.txt">Table of n, a(n) for n = 1..500</a>

%F G.f.: Sum_{n>=0}[(1-x^n)/(1-x)^n*Sum_{d|n}x^(n*d)].

%F a(n) ~ 2^(n-1). - _Vaclav Kotesovec_, May 01 2014

%p b:= proc(n,t,g) option remember; `if` (n=0, `if` (irem(t, g)=0, 1, 0), add (b(n-i, t+1, min(i, g)), i=1..n)) end: a:= n-> b(n, 0, infinity): seq (a(n), n=1..40);  # _Alois P. Heinz_, Dec 15 2009

%t a[n_] := SeriesCoefficient[ Sum[(1-x^k)/(1-x)^k*Sum[x^(k*d), {d, Divisors[k]}], {k, 0, n}], {x, 0, n}]; Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Feb 24 2015 *)

%Y Cf. A168657.

%K easy,nonn

%O 1,3

%A _Vladeta Jovovic_, Dec 13 2009

%E More terms from _Alois P. Heinz_, Dec 15 2009