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A171625
Number of compositions of n such that the number of parts is divisible by the smallest part.
2
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
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
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Dec 13 2009
EXTENSIONS
More terms from Alois P. Heinz, Dec 15 2009
STATUS
approved