%I #63 Apr 28 2016 14:21:33
%S 1,2,4,12,26,60,144,324,728,1602,3576,7808,17068,36908,79520,170704,
%T 364794,777036,1649456,3491188,7367544,15513336,32584648,68307264,
%U 142904080,298448914,622235060,1295320004,2692583916,5589586996,11588905844,23999052692
%N Number of overcompositions of n.
%C Analog to overpartitions, here an overcomposition is defined to be a composition in which the first occurrence of each distinct number may be overlined (see example).
%C Also 1 together with the row sums of A235999.
%C For the number of partitions of n see A000041.
%C For the number of compositions of n see A011782.
%C For the number of overpartitions of n see A015128.
%C Note that there are several orderings of overcompositions, the same as the orderings of compositions, but apparently for every ordering of overcompositions there are also several suborderings according to the arrangements of the overlined parts. The same for overpartitions. See one of them in Example section.
%H Alois P. Heinz, <a href="/A236002/b236002.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{k=1..A003056(n)} 2^k*A235998(n,k), n >= 1.
%e For n = 4 the 26 overcompositions of 4 are: [4], [4'], [1,3], [1',3], [1,3'], [1',3'], [2,2], [2',2], [1,1,2], [1',1,2], [1,1,2'], [1',1,2'], [3,1], [3',1], [3,1'], [3',1'], [1,2,1], [1',2,1], [1,2',1], [1',2',1], [2,1,1], [2',1,1], [2,1',1], [2',1',1], [1,1,1,1], [1',1,1,1].
%Y Cf. A000041, A011782, A015128, A235998, A235999, A238439.
%K nonn
%O 0,2
%A _Omar E. Pol_, Jan 19 2014
%E a(7) corrected and more terms added, _Joerg Arndt_, Jan 20 2014
%E a(19)-a(31) from _Alois P. Heinz_, Jan 20 2014