A240560 - OEIS

A240560

a(n) = 2^n*E(n,1/2) + 2^(n+1)*E(n+1,0), where E(n,x) the Euler polynomials.

0, 0, 1, 0, -11, 0, 211, 0, -6551, 0, 303271, 0, -19665491, 0, 1704396331, 0, -190473830831, 0, 26684005437391, 0, -4581126864886571, 0, 946075012113714451, 0, -231406946026650896711, 0, 66164529094650835995511, 0, -21866924546405967976005251

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OFFSET

0,5

LINKS

Table of n, a(n) for n=0..28.

FORMULA

a(n) = skp(n, 0) + skp(n+1, -1), where skp(n, x) are the Swiss-Knife polynomials A153641.

a(n) = A122045(n) - A155585(n+1).

MAPLE

A240560 := n -> euler(n) + 2^(n+1)*euler(n+1, 0):

seq(A240560(n), n=0..28);

MATHEMATICA

skp[n_, x_] := Sum[Binomial[n, k]*EulerE[k]*If[n==k, 1, x^(n-k)], {k, 0, n}];

a[n_] := skp[n, 0] + skp[n+1, -1];

Table[a[n], {n, 0, 28}] (* Jean-François Alcover, Jul 08 2019 *)

CROSSREFS

Cf. A122045, A155585, A240559, A240561.

Sequence in context: A261173 A287468 A110417 * A082258 A075361 A287630

Adjacent sequences: A240557 A240558 A240559 * A240561 A240562 A240563

KEYWORD

sign

AUTHOR

Peter Luschny, Apr 17 2014

STATUS

approved