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%I #4 Nov 18 2024 13:01:12
%S 1,1,-3,-26,1185,15376,-2749355,-49816976,22790134017,533858404096,
%T -498990299504499,-14365294449638912,23891962452055766497,
%U 816609772823716089856,-2201371244223771530940315,-87139486416935710159898624,355987789164484245477279893505
%N a(n) = (-2*n)^n * Euler(n, (n - 1)/(2*n)) for n >= 1, and a(0) = 1. Main diagonal of A378066.
%F a(n) = Sum_{j=0..n} binomial(n, j)*Euler(j)*(-n)^j.
%p a := n -> ifelse(n = 0, 1, (-2*n)^n * euler(n, (n - 1)/(2*n))):
%p seq(a(n), n = 0..16);
%Y Cf. A378066.
%K sign
%O 0,3
%A _Peter Luschny_, Nov 17 2024