a(n) = Sum_{k=0..n} (k+1) * A026780(n, k).

Terms

a(0) =1a(1) =3a(2) =10a(3) =27a(4) =76a(5) =195a(6) =519a(7) =1299a(8) =3364a(9) =8311a(10) =21191a(11) =51981a(12) =131273a(13) =320715a(14) =804845a(15) =1961823a(16) =4901782a(17) =11932489a(18) =29719325a(19) =72291325a(20) =179610365a(21) =436699813a(22) =1082870377a(23) =2632116551a(24) =6516122403a(25) =15835522783a(26) =39147779575