a(n) has generating function 1/((1-x)^k*(1-x^2)^(k*(k-1)/2)) for k=6.

Terms

a(0) =1a(1) =6a(2) =36a(3) =146a(4) =561a(5) =1812a(6) =5552a(7) =15372a(8) =40677a(9) =100562a(10) =239316a(11) =541926a(12) =1188341a(13) =2507736a(14) =5149056a(15) =10251560a(16) =19935135a(17) =37790610a(18) =70187260a(19) =127580310a(20) =227779695a(21) =399218820a(22) =688680720a(23) =1169024220a(24) =1956567795a(25) =3228473430a(26) =5260188780a(27) =8462889330a(28) =13461037155