a(n) = floor(exp(2/3)*n!).

Terms

a(0) =1a(1) =3a(2) =11a(3) =46a(4) =233a(5) =1402a(6) =9816a(7) =78532a(8) =706793a(9) =7067937a(10) =77747310a(11) =932967722a(12) =12128580386a(13) =169800125411