a(n) = Sum_{k=0..n} 2^k*p(k), where p(k) is the partition function A000041.

Terms

a(0) =1a(1) =3a(2) =11a(3) =35a(4) =115a(5) =339a(6) =1043a(7) =2963a(8) =8595a(9) =23955a(10) =66963a(11) =181651a(12) =497043a(13) =1324435a(14) =3536275a(15) =9303443a(16) =24442259a(17) =63370643a(18) =164296083a(19) =421197203a(20) =1078654355a(21) =2739598739a(22) =6942291347a(23) =17469994387a(24) =43894109587a(25) =109593687443a(26) =273070880147a(27) =677066241427