Total number of domino tilings of Ferrers-Young diagrams summed over all partitions of 2n.

Terms

a(0) =1a(1) =2a(2) =6a(3) =16a(4) =42a(5) =106a(6) =268a(7) =650a(8) =1580a(9) =3750a(10) =8862a(11) =20598a(12) =47776a(13) =109248a(14) =248966a(15) =562630a(16) =1264780a(17) =2823958a(18) =6282198a(19) =13884820a(20) =30590124a(21) =67051982a(22) =146463790a(23) =318588916a(24) =690882926a(25) =1492592450a(26) =3215372064a(27) =6904561416a(28) =14786529836a(29) =31574656096