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

0,3

Links

Table of n, a(n) for n=0..35.

Formula

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

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);

Prog

(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)]

Crossrefs

Cf. A000108, A002054, A238762, A323844.

Sequence in context: A085043 A338586 A143818 * A286258 A297446 A154918

Adjacent sequences: A238876 A238877 A238878 * A238880 A238881 A238882

Keyword

nonn

Author

Peter Luschny, Mar 06 2014

Status

approved