%I #11 Mar 09 2017 14:48:35

%S 1,1,2,4,7,14,26,50,95,180,343,652,1240,2359,4486,8532,16227,30862,

%T 58697,111636,212321,403814,768015,1460691,2778094,5283667,10049027,

%U 19112282,36349721,69133673,131485594,250072951,475614693,904573387,1720411555,3272057256,6223138101,11835809946,22510571803,42812941849

%N Expansion of 1/(1 - x - Sum_{k>=1} x^prime(k)).

%C Number of compositions (ordered partitions) of n into prime parts (1 included) (A008578).

%H Indranil Ghosh, <a href="/A280917/b280917.txt">Table of n, a(n) for n = 0..99</a>

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

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

%e a(4) = 7 because we have [3, 1], [2, 2], [2, 1, 1], [1, 3], [1, 2, 1], [1, 1, 2] and [1, 1, 1, 1].

%t nmax = 39; CoefficientList[Series[1/(1 - x - Sum[x^Prime[k], {k, 1, nmax}]), {x, 0, nmax}], x]

%o (PARI) Vec(1 / (1 - x - sum(k=1, 100, x^prime(k))) + O(x^100)) \\ _Indranil Ghosh_, Mar 09 2017

%Y Cf. A000607, A002124, A008578, A023360, A034891, A036497.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jan 10 2017