Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #18 Oct 17 2016 16:37:56
%S 0,0,1,4,6,10,20,1,36,172,2192,3371,1,22327,135561,517656,284492,
%T 933118,5446991,24265724,18238138,93800069,334654476,1368408363,
%U 2584589232,1823879615,25669818480,41583822879,1967330543,29409700520,1265785403,3239855363874
%N Arithmetic derivatives of the Motzkin numbers.
%F a(n) = A003415(A001006(n)).
%F a(n) = 1 for n in A092831.
%t 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 *)
%Y Cf. A003415, A001006, A068329, A092831.
%K nonn
%O 0,4
%A _Paul Bedard_, Oct 16 2016
%E More terms from _Alois P. Heinz_, Oct 16 2016