A171609 a(2*n) = (n+1)*a(n), a(2*n+1) = (n+1)*a(n+1), with a(1) = 1.

1, 2, 4, 6, 12, 16, 24, 30, 60, 72, 96, 112, 168, 192, 240, 270, 540, 600, 720, 792, 1056, 1152, 1344, 1456, 2184, 2352, 2688, 2880, 3600, 3840, 4320, 4590, 9180, 9720, 10800, 11400, 13680, 14400, 15840, 16632, 22176, 23232, 25344, 26496, 30912, 32256, 34944, 36400, 54600, 56784

Offset

1,2

Comments

The left column of the matrix powers A171608^n in the limit n->oo. (The other columns all become 0.)

Links

Table of n, a(n) for n=1..50.

Formula

Limit_{n->oo} (A171608)^n, a left-shifted vector considered as a sequence.

a(n+1) = a(n) * (1 + 1/A003602(n)). - Michael Somos, Dec 27 2022

Example

The cube of A171608 starts
   1  0  0  0  0  0  0  0  0  0
   2  0  0  0  0  0  0  0  0  0
   4  0  0  0  0  0  0  0  0  0
   6  0  0  0  0  0  0  0  0  0
  12  0  0  0  0  0  0  0  0  0
  16  0  0  0  0  0  0  0  0  0
  24  0  0  0  0  0  0  0  0  0
  30  0  0  0  0  0  0  0  0  0
   0 30  0  0  0  0  0  0  0  0
   0 36  0  0  0  0  0  0  0  0
... and the first 8 entries of the left column are already "converged." - R. J. Mathar, Sep 23 2021

Prog

(PARI) {a(n) = if(n < 2, n==0, (n\2 + 1)*a((n+1)\2))}; /* Michael Somos, Dec 27 2022 */

Crossrefs

Cf. A003602, A171608

Sequence in context: A089395 A089699 A089696 * A099316 A007416 A293132

Adjacent sequences: A171606 A171607 A171608 * A171610 A171611 A171612

Keyword

nonn

Author

Gary W. Adamson, Dec 12 2009

Extensions

More terms from R. J. Mathar, Sep 23 2021

Name changed by Michael Somos, Dec 27 2022

Status

approved