P(P(n))-P(P(n-1)), where P(n) = n(n+1)(n+2)/6 (cf. A000292).

Terms

a(0) =0a(1) =1a(2) =19a(3) =200a(4) =1320a(5) =6230a(6) =23086a(7) =71484a(8) =192900a(9) =467115a(10) =1036585a(11) =2140996a(12) =4164524a(13) =7698600a(14) =13623260a(15) =23210440a(16) =38252856a(17) =61222389a(18) =95462175a(19) =145416880a(20) =216905920a(21) =317444666a(22) =456618954a(23) =646518500a(24) =902235100a(25) =1242431775a(26) =1689989301a(27) =2272736844