[FORGED] How to write an estimated seasonal ARIMA model from R output?

I'm trying to use the following command.
arima (x, order = c(p,d,q), seasonal =list(order=c(P,D,Q), period=s)

How can I write an estimated seasonal ARIMA model from the outputs. To be specifically, which sign to use? I know R uses a different signs from S plus.

Is it correct that the model is:
(1-ar1*B-ar2*B^2-...)(1-sar1*B^s-sar2*B^2s-....)(1-B)^d(1-B^s)^D X_t=(1+ma1*B+ma2*B^2+...)(1+sma1*B^s+sma2*B^2s+....) a_t

For example:

m1=arima(koeps,order=c(0,1,1),seasonal=list(order=c(0,1,1),period=4))
m1

Call:
arima(x = koeps, order = c(0, 1, 1), seasonal = list(order = c(0, 1, 1), period = 4))
Coefficients:
           ma1     sma1
       -0.4096  -0.8203
s.e.   0.0866   0.0743

Should the estimated model be written as:
(1-B)(1-B^4) X_t=(1-0.4096B)(1-0.8203B^4) a_t
or (1-B)(1-B^4) X_t=(1+0.4096B)(1+0.8203B^4) a_t

Thanks!

The definition used here has

X[t] = a[1]X[t-1] + ? + a[p]X[t-p] + e[t] + b[1]e[t-1] + ? + b[q]e[t-q]