A338000 - OEIS

%I #12 Oct 21 2020 14:17:31

%S 0,0,2,4,1,1,151,604,1135,3652,163921,983020,4781635,26455096,

%T 880441381,7019296864,62338135855,485246558272,14909515819441,

%U 147911335595200,2005509679122475,19997668777814656,618177354753297901,7327199316870984064,135962126415847073095

%N a(n) = 2^floor((2-n)/2)*Sum_{0 <= k <= n and A337966(n, k) < 0} A173018(n, k).

%C The two sequences A337999 and A338000 represent the number of alternating permutations of order n as the difference between the greater and the smaller of the two absolute values (for n >= 2).

%F (A337999(n) - a(n))/2 = (-1)^floor(n/2)*A000111(n).

%F (-1)^floor(n/2)*(A337999(n) - a(n)) = A001250(n) for n >= 2.

%e Row 6 of A337967 is: 1, 57, -302, -302, 57, 1, 0. The sum of negative terms is 2*302 = 604. Thus a(6) = 604/4 = 151.

%p A338000 := n -> add(`if`(A337966(n,k)<0, A173018(n,k), 0), k=0..n)/2^floor((n-2)/2): seq(A338000(n), n=0..24);

%Y Cf. A337966, A337967, A173018, A337999, A000111, A001250.

%K nonn

%O 0,3

%A _Peter Luschny_, Oct 06 2020