A309801 If 2*n = Sum (2^e_k) then a(n) = Sum (e_k^n).

1, 4, 9, 81, 244, 793, 2316, 65536, 262145, 1049600, 4196353, 17308657, 68703188, 273234809, 1088123500, 152587890625, 762939453126, 3814697527769, 19073486852414, 95370918425026, 476847618556329, 2384217176269538, 11921023106645561, 59886119752101281

Offset

1,2

Comments

Replace 2^k with (k + 1)^n in binary representation of n.

Links

Table of n, a(n) for n=1..24.

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

Cf. A008935, A029931, A104258.

Sequence in context: A061104 A082381 A155931 * A248245 A368629 A077530

Adjacent sequences: A309798 A309799 A309800 * A309802 A309803 A309804

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 17 2019

Status

approved