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A238879
Row sums of the triangle of generalized ballot numbers A238762.
3
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
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
KEYWORD
nonn
AUTHOR
Peter Luschny, Mar 06 2014
STATUS
approved