A371684 a(n) = Sum_{k=0..n} 2^(3*k)*binomial(2*n, 2*k)*Euler(2*k, 1/2). Alternating row sums of A371637.

1, -1, 9, -217, 9841, -717841, 76804665, -11330490025, 2204195526241, -546715992537505, 168397490614671849, -63062013420332052985, 28216110792407667898321, -14866226664969958126495921, 9109882748673411939937074969, -6424247756451800785395922510537

Offset: 0

Author

Peter Luschny, Apr 03 2024

Keywords

• sign

Crossrefs

Cf. A371637, A371683.

Programs

Maple

seq(add(2^(3*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, 20}] (* Paolo Xausa, Apr 17 2024 *)

Formula

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