A343846 - OEIS

%I #17 May 06 2021 12:20:24

%S 0,2,6,40,350,4032,56364,933504,17824950,385848320,9334057876,

%T 249576198144,7308698191340,232643283353600,7997684730384600,

%U 295306112919306240,11655857682806336550,489743069731226910720,21824608434847162167300,1028154317960939805081600

%N a(n) = binomial(2*n, n)*2^n*|Euler(n, 1/2) - Euler(n, 0)|.

%F a(n) = binomial(2*n, n) * |Euler(n) - 2^n*Euler(n, 0)|.

%F a(n) = A109449(2*n, n) for n >= 1.

%F a(n) = (-1)^binomial(n, 2) * binomial(2*n, n) * A163747(n).

%F a(n) ~ 2^(3*n + 5/2) * n^n / (Pi^(n+1) * exp(n)). - _Vaclav Kotesovec_, May 06 2021

%p a := n -> binomial(2*n, n)*abs(euler(n) - 2^n*euler(n, 0)):

%p seq(a(n), n=0..19);

%t Table[Binomial[2*n, n]*Abs[EulerE[n] - 2^n*EulerE[n, 0]], {n, 0, 20}] (* _Vaclav Kotesovec_, May 06 2021 *)

%Y Cf. A109449, A163747.

%K nonn

%O 0,2

%A _Peter Luschny_, May 06 2021