A097940 - OEIS

%I #14 Jun 12 2019 06:34:07

%S 1,4,8,20,37,86,173,372,788,1680,3550,7554,15994,33820,71374,150376,

%T 316151,663474,1389760,2906116,6066899,12645608,26318870,54700044,

%U 113536171,235363832,487342781,1007969620,2082597193,4298660754

%N Sum of smallest parts (counted with multiplicity) of all compositions of n.

%H Alois P. Heinz, <a href="/A097940/b097940.txt">Table of n, a(n) for n = 1..400</a>

%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. 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*x^k/(1-x-x^k)^2, k=1..infinity).

%F a(n) ~ n * 2^(n-3). - _Vaclav Kotesovec_, Sep 05 2014

%F a(n) = Sum_{k=1..n} A308630(n,k). - _R. J. Mathar_, Jun 12 2019

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

%Y Cf. A046746, A092309.

%K easy,nonn

%O 1,2

%A _Vladeta Jovovic_, Sep 05 2004

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