Number of ballot sequences of length n having exactly three descents.

Terms

a(0) =1a(1) =17a(2) =145a(3) =836a(4) =3846a(5) =15002a(6) =52132a(7) =164576a(8) =484609a(9) =1337597a(10) =3521517a(11) =8850458a(12) =21485321a(13) =50358968a(14) =114911640a(15) =255114977a(16) =554333346a(17) =1178070741a(18) =2459840199a(19) =5042845917a(20) =10185374250a(21) =20257833206a(22) =39778823250a(23) =77088115856a(24) =147739793527a(25) =279923493220