|
%I #17 May 23 2020 14:30:47
%S 1,1,1,2,3,3,3,4,6,8,11,15,19,22,25,30,37,47,62,83,108,136,168,205,
%T 247,295,354,429,524,642,789,972,1196,1466,1789,2173,2625,3155,3778,
%U 4515,5391,6437,7692,9201,11014,13186,15780,18865,22516,26818,31871,37791
%N Number of compositions of n such that the smallest part is divisible by the number of parts.
%H Alois P. Heinz, <a href="/A171628/b171628.txt">Table of n, a(n) for n = 1..900</a>
%F G.f.: Sum_{n>=0} [Sum_{d|n} x^(n*d)*(1-x^d)/(1-x)^d].
%p b:= proc(n,t,g) option remember; `if` (n=0, `if` (irem(g, t)=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..60); # _Alois P. Heinz_, Dec 15 2009
%p A171628 := proc(n) local g,k; g := 0 ; for k from 0 to n do g := g+add (x^(k*d)*(1-x^d)/(1-x)^d,d=numtheory[divisors](k)) ; g := expand(g) ; end do ; coeftayl(g,x=0,n) ; end proc: seq(A171628(n),n=1..60) ; # _R. J. Mathar_, Dec 14 2009
%t b[n_, t_, g_] := b[n, t, g] = If[n == 0, If [Mod[g, t] == 0, 1, 0], Sum[b[n - i, t + 1, Min[i, g]], {i, n}]];
%t a[n_] := b[n, 0, Infinity];
%t Array[a, 60] (* _Jean-François Alcover_, May 23 2020, after _Alois P. Heinz_ *)
%Y Cf. A168656, A171625.
%K easy,nonn
%O 1,4
%A _Vladeta Jovovic_, Dec 13 2009
%E More terms from _R. J. Mathar_ and _Alois P. Heinz_, Dec 14 2009
|
