cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A097940 Sum of smallest parts (counted with multiplicity) of all compositions of n.

This page as a plain text file.
%I A097940 #19 Oct 15 2024 17:16:36
%S A097940 1,4,8,20,37,86,173,372,788,1680,3550,7554,15994,33820,71374,150376,
%T A097940 316151,663474,1389760,2906116,6066899,12645608,26318870,54700044,
%U A097940 113536171,235363832,487342781,1007969620,2082597193,4298660754,8864505305,18263797648,37597869188
%N A097940 Sum of smallest parts (counted with multiplicity) of all compositions of n.
%H A097940 Alois P. Heinz, <a href="/A097940/b097940.txt">Table of n, a(n) for n = 1..1000</a>
%H A097940 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 A097940 G.f.: (1-x)^2 * Sum_{k>=1} k*x^k/(1-x-x^k)^2.
%F A097940 a(n) ~ n * 2^(n-3). - _Vaclav Kotesovec_, Sep 05 2014
%F A097940 a(n) = Sum_{k=1..n} A308630(n,k). - _R. J. Mathar_, Jun 12 2019
%t A097940 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 A097940 Cf. A046746, A092309.
%K A097940 easy,nonn
%O A097940 1,2
%A A097940 _Vladeta Jovovic_, Sep 05 2004
%E A097940 More terms from _Robert G. Wilson v_, Sep 08 2004