A171625 Number of compositions of n such that the number of parts is divisible by the smallest part.

1, 1, 3, 7, 15, 29, 58, 118, 242, 493, 997, 2005, 4024, 8071, 16183, 32439, 65003, 130214, 260768, 522084, 1045045, 2091489, 4185209, 8373979, 16753651, 33516419, 67047467, 134118462, 268274858, 536611011, 1073321222, 2146803124, 4293866550, 8588154649

Offset: 1

Author

Vladeta Jovovic, Dec 13 2009

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A168657.

Programs

Maple

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

Mathematica

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 *)

Formula

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

a(n) ~ 2^(n-1). - Vaclav Kotesovec, May 01 2014

Extensions

More terms from Alois P. Heinz, Dec 15 2009