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

1,3

Links

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

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

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 *)

Crossrefs

Cf. A168657.

Sequence in context: A218189 A132780 A018087 * A284245 A153823 A283007

Adjacent sequences: A171622 A171623 A171624 * A171626 A171627 A171628

Keyword

easy,nonn

Author

Vladeta Jovovic, Dec 13 2009

Extensions

More terms from Alois P. Heinz, Dec 15 2009

Status

approved