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

0,4

Links

Table of n, a(n) for n=0..31.

Formula

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

a(n) = 1 for n in A092831.

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 *)

Crossrefs

Cf. A003415, A001006, A068329, A092831.

Sequence in context: A076995 A096817 A220033 * A320124 A185913 A243119

Adjacent sequences: A277452 A277453 A277454 * A277456 A277457 A277458

Keyword

nonn

Author

Paul Bedard, Oct 16 2016

Extensions

More terms from Alois P. Heinz, Oct 16 2016

Status

approved