Number of permutations p of [n] such that 0p has a nonincreasing jump sequence beginning with four.

Terms

a(0) =5a(1) =14a(2) =36a(3) =98a(4) =327a(5) =788a(6) =1890a(7) =4523a(8) =11483a(9) =27209a(10) =61983a(11) =139568a(12) =323531a(13) =730494a(14) =1618531a(15) =3543509a(16) =7851556a(17) =17204960a(18) =37331967a(19) =80312122a(20) =173234350a(21) =372183777a(22) =794587802a(23) =1686743710a(24) =3579347697a(25) =7578433425a(26) =15984149737a(27) =33580700124a(28) =70467297970a(29) =147600492302