A062798 Inverse Moebius transform of A001405 (binomial(n, floor(n/2))).
1, 3, 4, 9, 11, 26, 36, 79, 130, 265, 463, 956, 1717, 3470, 6449, 12949, 24311, 48772, 92379, 185027, 352755, 705897, 1352079, 2705182, 5200311, 10402319, 20058430, 40120076, 77558761, 155124243, 300540196, 601093339, 1166803576, 2333630533
Offset: 1
Keywords
Examples
For n = 9, divisors = {1,3,9}, a(9) = binomial(1, 0) + binomial(3, 1) + binomial(9, 4) = 1 + 3 + 126 = 130.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
a[n_] := DivisorSum[n, Binomial[#, Floor[#/2]]&]; Array[a, 35] (* Amiram Eldar, May 28 2025 *)
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PARI
a(n) = sumdiv(n, d, binomial(d, d\2)); \\ Amiram Eldar, May 28 2025
Formula
a(n) = Sum_{d|n} binomial(d, floor(d/2)).
Extensions
Offset corrected by Amiram Eldar, May 28 2025