A277455 Arithmetic derivatives of the Motzkin numbers.

0, 0, 1, 4, 6, 10, 20, 1, 36, 172, 2192, 3371, 1, 22327, 135561, 517656, 284492, 933118, 5446991, 24265724, 18238138, 93800069, 334654476, 1368408363, 2584589232, 1823879615, 25669818480, 41583822879, 1967330543, 29409700520, 1265785403, 3239855363874

Offset: 0

Author

Paul Bedard, Oct 16 2016

Keywords

• nonn

Crossrefs

Cf. A003415, A001006, A068329, A092831.

Programs

Mathematica

Table[If[Abs@ # < 2, 0, # Total[#2/#1 & @@@ FactorInteger[Abs@ #]]] &@ Hypergeometric2F1[(1 - n)/2, -n/2, 2, 4], {n, 0, 31}] (* Michael De Vlieger, Oct 17 2016, after Michael Somos at A003415 and Peter Luschny at A001006 *)

Formula

a(n) = A003415(A001006(n)).

a(n) = 1 for n in A092831.

Extensions

More terms from Alois P. Heinz, Oct 16 2016