Number of set partitions of [n] with alternating parity of elements and exactly four blocks.

Terms

a(0) =1a(1) =4a(2) =12a(3) =33a(4) =84a(5) =222a(6) =545a(7) =1425a(8) =3458a(9) =8948a(10) =21595a(11) =55335a(12) =133144a(13) =338530a(14) =813249a(15) =2056245a(16) =4935870a(17) =12432432a(18) =29833463a(19) =74952867a(20) =179842724a(21) =451071998a(22) =1082309293a(23) =2711584785a(24) =6506473162a(25) =16289249356a(26) =39088013091a(27) =97811687679a(28) =234720639024a(29) =587166227226