A238879 Row sums of the triangle of generalized ballot numbers A238762.

1, 1, 2, 5, 5, 21, 14, 84, 42, 330, 132, 1287, 429, 5005, 1430, 19448, 4862, 75582, 16796, 293930, 58786, 1144066, 208012, 4457400, 742900, 17383860, 2674440, 67863915, 9694845, 265182525, 35357670, 1037158320, 129644790, 4059928950, 477638700, 15905368710

Offset: 0

Author

Peter Luschny, Mar 06 2014

Keywords

• nonn

Crossrefs

Cf. A000108, A002054, A238762, A323844.

Programs

Maple

A238879 := proc(n) option remember;
if n < 2 then 1 else
   if n mod 2 = 0 then 1/(iquo(n,2)+2)
   else (2*n+4)/((n-1)*(n+5)) fi;
   % *(2*n+2)*A238879(n-2)
fi end:
seq(A238879(i), i = 0..30);

Sage

def f():
    f, g, b, n = 1, 1, 1, 1
    while True:
        n += 1
        if b == 1:
            yield g
            g *= 2*(n+1)/(n//2+2)
        else:
            yield f
            f *= 4*(n+1)*(n+2)/((n-1)*(n+5))
        b = 1 - b
A238879 = f(); [next(A238879) for n in range(31)]

Formula

a(2n) = A000108(n), a(2n+1) = A002054(n) (conjectured). - Ralf Stephan, Mar 14 2014