A258290 Arithmetic derivative of central binomial coefficients, cf. A000984.

0, 1, 5, 24, 59, 456, 1448, 6868, 19749, 69364, 236356, 1526956, 3717440, 22858340, 122553540, 474051984, 954720543, 5726109024, 19329586520, 92051285020, 319059863484, 1271796704788, 4829219746964, 29791326914640, 74372011398840, 340296661452300

Offset: 0

Author

Reinhard Zumkeller, May 26 2015

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000984, A003415, A258197.

Programs

Haskell

a258290 = a003415 . a000984

Mathematica

ad[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); ad[0] = ad[1] = 0; a[n_] := ad[Binomial[2*n, n]]; Array[a, 26, 0] (* Amiram Eldar, Apr 13 2025 *)

Formula

a(n) = A003415(A000984(n)).

Central terms in triangle A258197: a(n) = A258197(2*n,n).