A013309 exp(exp(x)-cos(x))=1+x+3/2!*x^2+8/3!*x^3+29/4!*x^4+112/5!*x^5...

1, 1, 3, 8, 29, 112, 489, 2326, 11937, 65856, 386561, 2406230, 15805473, 109131128, 789751577, 5972149246, 47079466913, 386051624736, 3286313327105, 28991306290278, 264621015301489, 2495440610319944