A304908 - OEIS

%I #6 May 21 2018 11:27:35

%S 0,1,4,9,24,50,108,217,448,882,1740,3366,6504,12428,23660,44745,84352,

%T 158270,296064,551950,1026360,1903524,3522596,6504998,11990160,

%U 22061700,40528748,74343096,136183488,249145148,455265420,830985473,1515201792,2760087990,5023154832,9133857670

%N Expansion of x * (d/dx) 1/(1 - Sum_{k>=0} x^(2^k)).

%C Sum of all parts of all compositions (ordered partitions) of n into powers of 2.

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

%F a(n) = n*A023359(n).

%t nmax = 35; CoefficientList[Series[x D[1/(1 - Sum[x^2^k, {k, 0, Floor[Log[nmax]/Log[2]] + 1}]), x], {x, 0, nmax}], x]

%t a[0] = 1; a[n_] := a[n] = Sum[Boole[k == 2^IntegerExponent[k, 2]] a[n - k], {k, 1, n}]; Table[n a[n], {n, 0, 35}]

%Y Cf. A000079, A001787, A023359, A036987, A281811, A304797, A303666, A304909.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, May 20 2018