A027982 Sum{(k+1)*T(n,2n-k)}, 0<=k<=2n, T given by A027960.

1, 10, 38, 108, 270, 632, 1426, 3148, 6854, 14784, 31674, 67508, 143278, 303016, 638882, 1343388, 2817942, 5898128, 12320650, 25689988, 53477246, 111148920, 230686578, 478150508, 989855590, 2046820192, 4227858266