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A248836 Number of length n arrays x(i), i=1..n with x(i) in 0..i and no value appearing more than 2 times.

%I A248836 #27 Jun 28 2025 12:56:25
%S A248836 1,2,6,22,96,482,2736,17302,120576,917762,7574016,67354582,642041856,
%T A248836 6530291042,70589700096,808090395862,9766250151936,124258689304322,
%U A248836 1660195646078976,23239748527125142,340125128186658816,5194627679316741602,82645634692238278656
%N A248836 Number of length n arrays x(i), i=1..n with x(i) in 0..i and no value appearing more than 2 times.
%C A248836 Column 2 of A248842
%H A248836 R. H. Hardin, <a href="/A248836/b248836.txt">Table of n, a(n) for n = 0..210</a>
%F A248836 From _Seiichi Manyama_, Feb 17 2025: (Start)
%F A248836 Conjecture: E.g.f.: 1/(1 - sin(x))^2.
%F A248836 If the above conjecture is correct, the following general term is obtained:
%F A248836 a(n) = Sum_{k=0..n} (k+1)! * i^(n-k) * A136630(n,k), where i is the imaginary unit. (End)
%F A248836 Conjecture from _Mikhail Kurkov_, Jun 26 2025: (Start)
%F A248836 a(n) = R(n+1,0) where
%F A248836   R(0,0) = 1,
%F A248836   R(n,k) = Sum_{j=0..n-k-1} R(n-1,j) for 0 <= k < n,
%F A248836   R(n,n) = Sum_{j=0..n-1} R(n,j). (End)
%e A248836 Some solutions for n=6
%e A248836 ..1....1....1....1....1....0....1....0....0....0....1....0....1....1....1....0
%e A248836 ..0....2....2....0....2....2....2....2....2....1....1....1....2....0....0....1
%e A248836 ..0....3....0....1....2....1....2....1....1....1....0....3....0....1....2....0
%e A248836 ..1....4....0....0....4....2....0....3....3....2....3....3....4....0....0....2
%e A248836 ..4....0....3....4....3....4....4....0....1....5....4....2....2....2....2....4
%e A248836 ..5....6....4....5....4....0....3....6....6....5....0....2....5....4....4....4
%Y A248836 Cf. A000111, A248842.
%K A248836 nonn
%O A248836 0,2
%A A248836 _R. H. Hardin_, Oct 15 2014
%E A248836 a(0)=1 prepended by _Seiichi Manyama_, Feb 17 2025