A291982 - OEIS

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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

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OFFSET

0,2

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.

LINKS

Table of n, a(n) for n=0..18.

FORMULA

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

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}]

PROG

(Python)

from sympy import euler

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

CROSSREFS

Cf. A007814, A291897.

Sequence in context: A115647 A019437 A365505 * A309258 A163423 A291126

Adjacent sequences: A291979 A291980 A291981 * A291983 A291984 A291985

KEYWORD

nonn

AUTHOR

Peter Luschny, Sep 22 2017

STATUS

approved