a(n) = (1^n + 2^n +3^n + 4^n)/2.

Terms

a(0) =2a(1) =5a(2) =15a(3) =50a(4) =177a(5) =650a(6) =2445a(7) =9350a(8) =36177a(9) =141170a(10) =554325a(11) =2186750a(12) =8656377a(13) =34355690a(14) =136617405a(15) =544061750a(16) =2169039777a(17) =8654570210a(18) =34553579685a(19) =138020346350a(20) =551499730377