A343846 a(n) = binomial(2*n, n)*2^n*|Euler(n, 1/2) - Euler(n, 0)|.

0, 2, 6, 40, 350, 4032, 56364, 933504, 17824950, 385848320, 9334057876, 249576198144, 7308698191340, 232643283353600, 7997684730384600, 295306112919306240, 11655857682806336550, 489743069731226910720, 21824608434847162167300, 1028154317960939805081600

Offset: 0

Author

Peter Luschny, May 06 2021

Keywords

• nonn

Crossrefs

Cf. A109449, A163747.

Programs

Maple

a := n -> binomial(2*n, n)*abs(euler(n) - 2^n*euler(n, 0)):
seq(a(n), n=0..19);

Mathematica

Table[Binomial[2*n, n]*Abs[EulerE[n] - 2^n*EulerE[n, 0]], {n, 0, 20}] (* Vaclav Kotesovec, May 06 2021 *)

Formula

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

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

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

a(n) ~ 2^(3*n + 5/2) * n^n / (Pi^(n+1) * exp(n)). - Vaclav Kotesovec, May 06 2021