A027043 a(n) = Sum{(k+1)*T(n,k)}, 0<=k<=2n, T given by A027023.

1, 6, 23, 80, 285, 990, 3367, 11256, 37097, 120862, 390123, 1249728, 3978365, 12598350, 39718403, 124743104, 390491505, 1218875302, 3794984883, 11789335464, 36551285573, 113120066678, 349523991123, 1078402178776