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%I #11 Apr 17 2024 03:23:25
%S 1,-1,9,-217,9841,-717841,76804665,-11330490025,2204195526241,
%T -546715992537505,168397490614671849,-63062013420332052985,
%U 28216110792407667898321,-14866226664969958126495921,9109882748673411939937074969,-6424247756451800785395922510537
%N a(n) = Sum_{k=0..n} 2^(3*k)*binomial(2*n, 2*k)*Euler(2*k, 1/2). Alternating row sums of A371637.
%F a(n) ~ (-1)^n * cos(Pi/(2*sqrt(2))) * 2^(5*n+3) * n^(2*n + 1/2) / (Pi^(2*n + 1/2) * exp(2*n)). - _Vaclav Kotesovec_, Apr 03 2024
%p seq(add(2^(3*k)*binomial(2*n, 2*k)*euler(2*k, 1/2), k = 0..n), n = 0..15);
%t Table[Sum[2^(3*k)*Binomial[2*n, 2*k]*EulerE[2*k, 1/2], {k, 0, n}], {n, 0, 20}] (* _Paolo Xausa_, Apr 17 2024 *)
%Y Cf. A371637, A371683.
%K sign
%O 0,3
%A _Peter Luschny_, Apr 03 2024
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