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Like this

sage: y = polygen(QQ,'y')
sage: x = LazyPowerSeriesRing(y.parent(),'x').gen()
sage: f = exp(x * y) * sec(x)
sage: [list(f[n]*factorial(n)) for n in range(10)]
[[1],
 [0, 1],
 [1, 0, 1],
 [0, 3, 0, 1],
 [5, 0, 6, 0, 1],
 [0, 25, 0, 10, 0, 1],
 [61, 0, 75, 0, 15, 0, 1],
 [0, 427, 0, 175, 0, 21, 0, 1],
 [1385, 0, 1708, 0, 350, 0, 28, 0, 1],
 [0, 12465, 0, 5124, 0, 630, 0, 36, 0, 1]]