a(n) = 2^n * Sum_{k=0..n} k^p*q^k, where p=3, q=-1/2.

Terms

a(0) =0a(1) =-1a(2) =6a(3) =-15a(4) =34a(5) =-57a(6) =102a(7) =-139a(8) =234a(9) =-261a(10) =478a(11) =-375a(12) =978a(13) =-241a(14) =2262a(15) =1149a(16) =6394a(17) =7875a(18) =21582a(19) =36305a(20) =80610a(21) =151959a(22) =314566a(23) =616965a(24) =1247754a(25) =2479883a(26) =4977342a(27) =9935001a(28) =19891954a(29) =39759519