From a definite integral.

Terms

a(0) =1a(1) =5a(2) =10a(3) =30a(4) =74a(5) =199a(6) =515a(7) =1355a(8) =3540a(9) =9276a(10) =24276a(11) =63565a(12) =166405a(13) =435665a(14) =1140574a(15) =2986074a(16) =7817630a(17) =20466835a(18) =53582855a(19) =140281751a(20) =367262376a(21) =961505400a(22) =2517253800a(23) =6590256025a(24) =17253514249a(25) =45170286749a(26) =118257345970