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

%I #21 Dec 28 2022 09:13:33

%S 1,2,4,6,12,16,24,30,60,72,96,112,168,192,240,270,540,600,720,792,

%T 1056,1152,1344,1456,2184,2352,2688,2880,3600,3840,4320,4590,9180,

%U 9720,10800,11400,13680,14400,15840,16632,22176,23232,25344,26496,30912,32256,34944,36400,54600,56784

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

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

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

%F a(n+1) = a(n) * (1 + 1/A003602(n)). - _Michael Somos_, Dec 27 2022

%e The cube of A171608 starts

%e 1 0 0 0 0 0 0 0 0 0

%e 2 0 0 0 0 0 0 0 0 0

%e 4 0 0 0 0 0 0 0 0 0

%e 6 0 0 0 0 0 0 0 0 0

%e 12 0 0 0 0 0 0 0 0 0

%e 16 0 0 0 0 0 0 0 0 0

%e 24 0 0 0 0 0 0 0 0 0

%e 30 0 0 0 0 0 0 0 0 0

%e 0 30 0 0 0 0 0 0 0 0

%e 0 36 0 0 0 0 0 0 0 0

%e ... and the first 8 entries of the left column are already "converged." - _R. J. Mathar_, Sep 23 2021

%o (PARI) {a(n) = if(n < 2, n==0, (n\2 + 1)*a((n+1)\2))}; /* _Michael Somos_, Dec 27 2022 */

%Y Cf. A003602, A171608

%K nonn

%O 1,2

%A _Gary W. Adamson_, Dec 12 2009

%E More terms from _R. J. Mathar_, Sep 23 2021

%E Name changed by _Michael Somos_, Dec 27 2022

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Last modified July 13 12:04 EDT 2024. Contains 374282 sequences. (Running on oeis4.)