OFFSET
1,2
COMMENTS
Replace 2^k with (k + 1)^n in binary representation of n.
FORMULA
a(n) = [x^n] (1/(1 - x)) * Sum_{k>=0} (k + 1)^n*x^(2^k)/(1 + x^(2^k)).
EXAMPLE
14 = 2*7 = 2^1 + 2^2 + 2^3 so a(7) = 1^7 + 2^7 + 3^7 = 2316.
MATHEMATICA
Table[Reverse[#].Range[Length[#]]^n &@IntegerDigits[n, 2], {n, 1, 24}]
Table[SeriesCoefficient[1/(1 - x) Sum[(k + 1)^n x^2^k/(1 + x^2^k), {k, 0, Floor[Log[2, n]] + 1}], {x, 0, n}], {n, 1, 24}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 17 2019
STATUS
approved