cp's OEIS Frontend

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

%I A238879 #16 Mar 01 2020 07:46:47
%S A238879 1,1,2,5,5,21,14,84,42,330,132,1287,429,5005,1430,19448,4862,75582,
%T A238879 16796,293930,58786,1144066,208012,4457400,742900,17383860,2674440,
%U A238879 67863915,9694845,265182525,35357670,1037158320,129644790,4059928950,477638700,15905368710
%N A238879 Row sums of the triangle of generalized ballot numbers A238762.
%F A238879 a(2n) = A000108(n), a(2n+1) = A002054(n) (conjectured). - _Ralf Stephan_, Mar 14 2014
%p A238879 A238879 := proc(n) option remember;
%p A238879 if n < 2 then 1 else
%p A238879    if n mod 2 = 0 then 1/(iquo(n,2)+2)
%p A238879    else (2*n+4)/((n-1)*(n+5)) fi;
%p A238879    % *(2*n+2)*A238879(n-2)
%p A238879 fi end:
%p A238879 seq(A238879(i), i = 0..30);
%o A238879 (Sage)
%o A238879 def f():
%o A238879     f, g, b, n = 1, 1, 1, 1
%o A238879     while True:
%o A238879         n += 1
%o A238879         if b == 1:
%o A238879             yield g
%o A238879             g *= 2*(n+1)/(n//2+2)
%o A238879         else:
%o A238879             yield f
%o A238879             f *= 4*(n+1)*(n+2)/((n-1)*(n+5))
%o A238879         b = 1 - b
%o A238879 A238879 = f(); [next(A238879) for n in range(31)]
%Y A238879 Cf. A000108, A002054, A238762, A323844.
%K A238879 nonn
%O A238879 0,3
%A A238879 _Peter Luschny_, Mar 06 2014