Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #13 Apr 06 2024 14:58:15
%S 1,3,33,819,37281,2720643,291107457,42945429747,8354465297601,
%T 2072193715976067,638269648981638753,239021193599722872627,
%U 106946291677392350660961,56346809266835212819000323,34528790475992735166895973313,24349545528533035663737512791539
%N a(n) = Sum_{k=0..n} (-2)^(3*k)*binomial(2*n, 2*k)*Euler(2*k, 1/2). Row sums of A371637.
%F a(n) ~ cosh(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((-8)^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,0,15}] (* _James C. McMahon_, Apr 05 2024 *)
%Y Cf. A371637, A371684.
%K nonn
%O 0,2
%A _Peter Luschny_, Apr 03 2024