%I #15 Nov 11 2020 07:48:46

%S 1,1,3,2,8,13,21,38,89,173,302,545,1109,2309,4564,8601,16188,31365,

%T 62518,125813,251119,493123,956437,1854281,3633938,7218166,14444539,

%U 28868203,57300450,112921744,221760513,436117749,861764899,1711773936

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

%H Vaclav Kotesovec, <a href="/A171634/b171634.txt">Table of n, a(n) for n = 1..715</a> (terms 1..250 from Alois P. Heinz)

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

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

%t b[n_, t_, g_] := b[n, t, g] = If[n == 0, If [Mod[t, g] == 0, 1, 0], Sum[b[n - i, t + 1, Max[i, g]], {i, 1, n}]];

%t a[n_] := b[n, 0, 0];

%t Array[a, 40] (* _Jean-François Alcover_, Nov 11 2020, after _Alois P. Heinz_ *)

%Y Cf. A168659, A171632.

%K easy,nonn

%O 1,3

%A _Vladeta Jovovic_, Dec 13 2009

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