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a(n) = n*a(n-1) + n^signum(n mod 4), a(0) = 1.
3

%I #26 May 11 2024 21:54:59

%S 1,2,6,21,85,430,2586,18109,144873,1303866,13038670,143425381,

%T 1721104573,22374359462,313241032482,4698615487245,75177847795921,

%U 1278023412530674,23004421425552150,437084007085490869,8741680141709817381,183575282975906165022

%N a(n) = n*a(n-1) + n^signum(n mod 4), a(0) = 1.

%C This sequence is one of many possible solutions to puzzle 16 on the Meerdaelquiz puzzle page, cf. the Delestinne link and A090805.

%H Alois P. Heinz, <a href="/A344229/b344229.txt">Table of n, a(n) for n = 0..450</a>

%H Hugo Delestinne, <a href="http://users.skynet.be/lch/mquiz/mquiz%202003/vragen/mquiz_2003_tafelronde_2.htm">Meerdaelquiz</a> [broken link]

%H N. J. A. Sloane and Brady Haran, <a href="https://www.youtube.com/watch?v=0zT16q3p24M">A Sequence with a Mistake</a>, Numberphile video (2021)

%p a:= proc(n) a(n):= n*a(n-1) + n^signum(n mod 4) end: a(0):= 1:

%p seq(a(n), n=0..23);

%Y Cf. A000142, A000522, A010873, A033540, A053817, A057427, A090805, A166486, A277506.

%K nonn

%O 0,2

%A _Alois P. Heinz_, May 12 2021