A291982 a(n) = Euler(n, n+1) * 2^valuation(n+1, 2), where Euler(n, x) denotes the Euler polynomial.

1, 3, 6, 161, 380, 9251, 68922, 9718545, 24721272, 1140755269, 14712346550, 1678097074579, 13104139232340, 889926827467887, 16319429252249970, 10286621696853755681, 27076409740571217392, 2427916115944458451025, 57728302956904672126062

Offset: 0

Author

Peter Luschny, Sep 22 2017

Keywords

• nonn

Comments

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

This conjecture was inspired by Vladimir Shevelev's conjecture in A291897.

Crossrefs

Cf. A007814, A291897.

Programs

Maple

A291982 := n -> euler(n, n+1)*2^(padic[ordp](n+1, 2)):
seq(A291982(n), n=0..18);

Mathematica

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

Python

from sympy import euler
def A291982(n): return euler(n,n+1)*(n+1 & -n-1) # Chai Wah Wu, Jul 07 2022

Formula

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