From a definite integral.

Terms

a(0) =1a(1) =1a(2) =6a(3) =11a(4) =36a(5) =85a(6) =235a(7) =600a(8) =1590a(9) =4140a(10) =10866a(11) =28416a(12) =74431a(13) =194821a(14) =510096a(15) =1335395a(16) =3496170a(17) =9153025a(18) =23963005a(19) =62735880a(20) =164244756a(21) =429998256a(22) =1125750156a(23) =2947252056a(24) =7716006181a(25) =20200766305a(26) =52886292930a(27) =138458112275a(28) =362488044120