A274054 - OEIS

%I #33 Jun 19 2016 16:29:42

%S 1,1,0,1,3,6,14,40,140,422,1346,4487,15234,52632,183913,651948,

%T 2336751,8438406,30712379,112603500,415459873,1541646225,5750112809,

%U 21548036621,81096740799,306404247854,1161863199131,4420429256826,16869986745367,64567073382731

%N Number of modified skew Dyck paths of semilength n such that the area between the x-axis and the path is n*(n+1)/2.

%C A modified skew Dyck path is a path in the first quadrant which begins at the origin, ends on the x-axis, consists of steps U=(1,1) (up), D=(1,-1) (down) and A=(-1,1) (anti-down) so that A and D steps do not overlap.

%F a(n) = A274372(n,n*(n+1)/2) = A274372(n,A000217(n)).

%e a(1) = 1:   /\

%e .

%e             /\

%e             \ \

%e a(3) = 1:   /  \

%e .

%e                 /\                          /\

%e                /  \         /\/\/\         /  \

%e a(4) = 3:   /\/    \   ,   /      \   ,   /    \/\   .

%Y Cf. A000217, A230823, A274372.

%K nonn

%O 0,5

%A _Alois P. Heinz_, Jun 19 2016