From Apery continued fraction for zeta(3): zeta(3)=6/(5-1^6/(117-2^6/(535-3^6/(1463...)))).

Terms

a(0) =5a(1) =117a(2) =535a(3) =1463a(4) =3105a(5) =5665a(6) =9347a(7) =14355a(8) =20893a(9) =29165a(10) =39375a(11) =51727a(12) =66425a(13) =83673a(14) =103675a(15) =126635a(16) =152757a(17) =182245a(18) =215303a(19) =252135a(20) =292945a(21) =337937a(22) =387315a(23) =441283a(24) =500045a(25) =563805a(26) =632767a(27) =707135a(28) =787113a(29) =872905