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

Author

Labos Elemer, Jul 19 2001

Keywords

• nonn

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

Crossrefs

Cf. A001405, A062791, A072929.

Programs

Mathematica

a[n_] := DivisorSum[n, Binomial[#, Floor[#/2]]&]; Array[a, 35] (* Amiram Eldar, May 28 2025 *)

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