A308501 Partial products of odious numbers.

1, 1, 2, 8, 56, 448, 4928, 64064, 896896, 14350336, 272656384, 5725784064, 125967249408, 3149181235200, 81878712115200, 2292603939225600, 71070722115993600, 2274263107711795200, 79599208769912832000, 2945170724486774784000, 111916487530497441792000, 4588575988750395113472000

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..404

J.-P. Allouche, The zeta-regularized product of odious numbers, arXiv:1906.10532 [math.NT], 2019.

Formula

a(n) = Product_{k=1..n} A000069(k).

Mathematica

Join[{1}, FoldList[Times, Select[Range[0, 50], OddQ[DigitCount[#, 2, 1]]&]]] (* Harvey P. Dale, Aug 09 2024 *)

Prog

(PARI) f(n) = 2*n - 1 - hammingweight(n-1)%2; \\ A000069
a(n) = prod(k=1, n, f(k))

Crossrefs

Cf. A000069 (odious numbers).

Sequence in context: A291314 A354248 A366267 * A316142 A109618 A201128

Adjacent sequences: A308498 A308499 A308500 * A308502 A308503 A308504

Keyword

nonn

Author

Michel Marcus, Jun 26 2019

Status

approved