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A168655 Number of compositions such that the number of parts is divisible by the first part.

%I A168655 #17 Nov 14 2014 11:59:15
%S A168655 1,1,3,5,11,22,44,88,177,355,710,1419,2838,5679,11363,22727,45443,
%T A168655 90862,181703,363419,726903,1453875,2907667,5814880,11628864,23256828,
%U A168655 46513965,93031069,186068503,372142797,744280096,1488527555,2976987042,5953897971,11907811651
%N A168655 Number of compositions such that the number of parts is divisible by the first part.
%H A168655 Alois P. Heinz, <a href="/A168655/b168655.txt">Table of n, a(n) for n = 1..250</a>
%F A168655 G.f.: (1-x)*Sum(x^(2*n-1)/((1-x)^n-x^n),n=1..infinity), First differences of A101510.
%F A168655 a(n) ~ log(2) * 2^(n-1). - _Vaclav Kotesovec_, May 01 2014
%p A168655 b:= proc(n,t,g) option remember; `if`(n=0,
%p A168655       `if`(irem(t, g)=0, 1, 0), add(b(n-i, t+1,
%p A168655       `if`(g=0,i,g)), i=1..n))
%p A168655     end:
%p A168655 a:= n-> b(n,0,0):
%p A168655 seq(a(n), n=1..40); # _Alois P. Heinz_, Dec 15 2009
%t A168655 A101510[n_] := Sum[If[Mod[i+1, k+1] == 0, Binomial[n-k, i], 0], {k, 0, n/2}, {i, 0, n-k}]; A168655 =  Join[{1}, Table[A101510[n], {n, 0, 32}] // Differences] (* _Jean-François Alcover_, Jan 24 2014 *)
%Y A168655 Cf. A079501.
%K A168655 easy,nonn
%O A168655 1,3
%A A168655 _Vladeta Jovovic_, Dec 01 2009
%E A168655 More terms from _Alois P. Heinz_, Dec 15 2009