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A304908
Expansion of x * (d/dx) 1/(1 - Sum_{k>=0} x^(2^k)).
1
0, 1, 4, 9, 24, 50, 108, 217, 448, 882, 1740, 3366, 6504, 12428, 23660, 44745, 84352, 158270, 296064, 551950, 1026360, 1903524, 3522596, 6504998, 11990160, 22061700, 40528748, 74343096, 136183488, 249145148, 455265420, 830985473, 1515201792, 2760087990, 5023154832, 9133857670
OFFSET
0,3
COMMENTS
Sum of all parts of all compositions (ordered partitions) of n into powers of 2.
FORMULA
a(n) = n*A023359(n).
MATHEMATICA
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]
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}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 20 2018
STATUS
approved