%I #25 Oct 15 2024 17:14:04

%S 1,3,6,15,31,72,155,340,738,1595,3424,7335,15642,33243,70432,148808,

%T 313571,659188,1382682,2894369,6047397,12613209,26265098,54610722,

%U 113387831,235117449,486933645,1007290340,2081469759,4296789924,8861401891,18258651137,37589337434

%N Total number of smallest parts in all compositions of n.

%H Alois P. Heinz, <a href="/A097941/b097941.txt">Table of n, a(n) for n = 1..1000</a> (first 500 terms from Vincenzo Librandi)

%H Knopfmacher, Arnold; Munagi, Augustine O. <a href="https://doi.org/10.1007/978-3-642-30979-3_11">Smallest parts in compositions</a>, Kotsireas, Ilias S. (ed.) et al., Advances in combinatorics. In part based on the 3rd Waterloo workshop on computer algebra (WWCA, W80) 2011, Waterloo, Canada, May 26-29, 2011. Berlin: Springer. 197-207 (2013).

%F G.f.: (1-x)^2 * Sum_{k>=1} x^k/(1-x-x^k)^2.

%F a(n) ~ n*2^(n-3). - _Vaclav Kotesovec_, Apr 30 2014

%F a(n) = Sum_{k=0..n} k * A238342(n,k). - _Alois P. Heinz_, Oct 15 2024

%t Drop[ CoefficientList[ Series[(1 - x)^2*Sum[x^k/(1 - x - x^k)^2, {k, 50}], {x, 0, 30}], x], 1] (* _Robert G. Wilson v_, Sep 08 2004 *)

%Y Cf. A092269, A097939, A097940, A238342.

%K easy,nonn

%O 1,2

%A _Vladeta Jovovic_, Sep 05 2004

%E More terms from _Robert G. Wilson v_, Sep 08 2004