A238879 - OEIS

%I #16 Mar 01 2020 07:46:47

%S 1,1,2,5,5,21,14,84,42,330,132,1287,429,5005,1430,19448,4862,75582,

%T 16796,293930,58786,1144066,208012,4457400,742900,17383860,2674440,

%U 67863915,9694845,265182525,35357670,1037158320,129644790,4059928950,477638700,15905368710

%N Row sums of the triangle of generalized ballot numbers A238762.

%F a(2n) = A000108(n), a(2n+1) = A002054(n) (conjectured). - _Ralf Stephan_, Mar 14 2014

%p A238879 := proc(n) option remember;

%p if n < 2 then 1 else

%p    if n mod 2 = 0 then 1/(iquo(n,2)+2)

%p    else (2*n+4)/((n-1)*(n+5)) fi;

%p    % *(2*n+2)*A238879(n-2)

%p fi end:

%p seq(A238879(i), i = 0..30);

%o (Sage)

%o def f():

%o     f, g, b, n = 1, 1, 1, 1

%o     while True:

%o         n += 1

%o         if b == 1:

%o             yield g

%o             g *= 2*(n+1)/(n//2+2)

%o         else:

%o             yield f

%o             f *= 4*(n+1)*(n+2)/((n-1)*(n+5))

%o         b = 1 - b

%o A238879 = f(); [next(A238879) for n in range(31)]

%Y Cf. A000108, A002054, A238762, A323844.

%K nonn

%O 0,3

%A _Peter Luschny_, Mar 06 2014