%I #16 Jul 08 2022 08:22:55

%S 1,3,6,161,380,9251,68922,9718545,24721272,1140755269,14712346550,

%T 1678097074579,13104139232340,889926827467887,16319429252249970,

%U 10286621696853755681,27076409740571217392,2427916115944458451025,57728302956904672126062

%N a(n) = Euler(n, n+1) * 2^valuation(n+1, 2), where Euler(n, x) denotes the Euler polynomial.

%C Conjecture: If n >= 2 is even then n*(n+1) divides a(n).

%C This conjecture was inspired by _Vladimir Shevelev_'s conjecture in A291897.

%F a(n) = Euler(n, n+1)*2^A007814(n+1).

%p A291982 := n -> euler(n, n+1)*2^(padic[ordp](n+1, 2)):

%p seq(A291982(n), n=0..18);

%t Table[2^IntegerExponent[n+1, 2] EulerE[n, n+1], {n, 1, 15}]

%o (Python)

%o from sympy import euler

%o def A291982(n): return euler(n,n+1)*(n+1 & -n-1) # _Chai Wah Wu_, Jul 07 2022

%Y Cf. A007814, A291897.

%K nonn

%O 0,2

%A _Peter Luschny_, Sep 22 2017