a(n) = Sum_{i=0..n} Sum_{j=0..n} (-1)^(i+j) * (i+j)!/(i!j!).

Terms

a(0) =1a(1) =1a(2) =3a(3) =9a(4) =31a(5) =111a(6) =407a(7) =1513a(8) =5679a(9) =21471a(10) =81643a(11) =311895a(12) =1196131a(13) =4602235a(14) =17757183a(15) =68680169a(16) =266200111a(17) =1033703055a(18) =4020716123a(19) =15662273839a(20) =61092127491a(21) =238582873475a(22) =932758045123