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

Terms

a(0) =1a(1) =3a(2) =10a(3) =28a(4) =80a(5) =211a(6) =569a(7) =1455a(8) =3806a(9) =9564a(10) =24565a(11) =61080a(12) =155041a(13) =382920a(14) =964163a(15) =2370712a(16) =5934974a(17) =14548685a(18) =36266755a(19) =88711181a(20) =220415107a(21) =538305745a(22) =1334040167a(23) =3254193849a(24) =8047710361a(25) =19613210297a(26) =48419611161