%I #12 Jul 11 2021 03:45:47

%S 1,1,3,2,6,9,15,22,41,68,118,199,337,571,982,1677,2860,4866,8284,

%T 14084,23911,40544,68679,116172,196249,331096,557927,939008,1578450,

%U 2650167,4444505,7445658,12460248,20830822,34790302,58049613,96771364,161182065

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

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

%H Alois P. Heinz, <a href="/A171632/b171632.txt">Table of n, a(n) for n = 1..250</a>

%p b:= proc(n,t,g) option remember; `if` (n=0, `if` (irem(g, t)=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[g, t] == 0, 1, 0],

%t Sum[b[n - i, t + 1, Max[i, g]], {i, 1, n}]];

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

%t Table [a[n], {n, 1, 40}] (* _Jean-François Alcover_, Jul 11 2021, after _Alois P. Heinz_ *)

%Y Cf. A168659.

%K easy,nonn

%O 1,3

%A _Vladeta Jovovic_, Dec 13 2009

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