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A214447 (-2)^n * Euler_polynomial(n,1) * binomial(2*n,n). 2
1, -2, 0, 40, 0, -4032, 0, 933504, 0, -385848320, 0, 249576198144, 0, -232643283353600, 0, 295306112919306240, 0, -489743069731226910720, 0, 1028154317960939805081600, 0, -2665182817368374114506506240, 0, 8360422228704533182913131315200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Central column of the Euler tangent triangle, a(n) = A081733(2*n,n).

Also a(n) = -A162660(2*n,n) for n > 0. - Peter Luschny, Jul 23 2012

LINKS

Table of n, a(n) for n=0..23.

FORMULA

a(n) = [x^n](skp(2*n,x+1)-skp(2*n,x-1))/2) where skp(n,x) are the Swiss-Knife polynomials A153641.

a(n) = (n+1)*2^n*(2*n-1)!!*sum_{k=1..n}sum_{j=0..k}(-1)^(k-j)*(k-j)^n/(j!*(n-j+1)!)  for n > 0. - Peter Luschny, Jul 23 2012

MAPLE

A214447 := n -> binomial(2*n, n)*(-2)^n*euler(n, 1):

seq(A214447(n), n=0..23);

PROG

(Sage)

from mpmath import *

mp.dps = 32

def A214447(n) : return (n+1)*2^n*fac2(2*n-1)*add(add((-1)^(k-j)*(k-j)^n / (factorial(j)*factorial(n-j+1)) for j in (0..k)) for k in (1..n))

[round(A214447(n)) for n in (0..9)] # Peter Luschny, Jul 23 2012

CROSSREFS

A081733, A214445.

Sequence in context: A120489 A145576 A178235 * A230888 A185281 A012445

Adjacent sequences:  A214444 A214445 A214446 * A214448 A214449 A214450

KEYWORD

sign

AUTHOR

Peter Luschny, Jul 18 2012

STATUS

approved

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Last modified February 15 20:32 EST 2019. Contains 320138 sequences. (Running on oeis4.)