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 A309801 If 2*n = Sum (2^e_k) then a(n) = Sum (e_k^n). 0
 1, 4, 9, 81, 244, 793, 2316, 65536, 262145, 1049600, 4196353, 17308657, 68703188, 273234809, 1088123500, 152587890625, 762939453126, 3814697527769, 19073486852414, 95370918425026, 476847618556329, 2384217176269538, 11921023106645561, 59886119752101281 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Replace 2^k with (k + 1)^n in binary representation of n. LINKS 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 A077530 A115551 Adjacent sequences:  A309798 A309799 A309800 * A309802 A309803 A309804 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Aug 17 2019 STATUS approved

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Last modified April 20 05:31 EDT 2021. Contains 343121 sequences. (Running on oeis4.)