A371683 a(n) = Sum_{k=0..n} (-2)^(3*k)*binomial(2*n, 2*k)*Euler(2*k, 1/2). Row sums of A371637.

1, 3, 33, 819, 37281, 2720643, 291107457, 42945429747, 8354465297601, 2072193715976067, 638269648981638753, 239021193599722872627, 106946291677392350660961, 56346809266835212819000323, 34528790475992735166895973313, 24349545528533035663737512791539

Offset: 0

Author

Peter Luschny, Apr 03 2024

Keywords

• nonn

Crossrefs

Cf. A371637, A371684.

Programs

Maple

seq(add((-8)^k*binomial(2*n, 2*k)*euler(2*k, 1/2), k = 0..n), n = 0..15);

Mathematica

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 *)

Formula

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