A187916 a(n) = C(n) if n is odd, else C(n) - C(n/2); C(n) are Catalan numbers.

1, 1, 5, 12, 42, 127, 429, 1416, 4862, 16754, 58786, 207880, 742900, 2674011, 9694845, 35356240, 129644790, 477633838, 1767263190, 6564103624, 24466267020, 91482504854, 343059613650, 1289903939312, 4861946401452, 18367352329252, 69533550916004

Offset: 1

Author

Gary W. Adamson, Mar 15 2011

Keywords

• nonn
• easy

Examples

			a(6) = 127 = A000108(6) - A000108(3) = (132 - 5)
a(5) = 42 = A000108(5)
		

Crossrefs

Cf. A000912, A000108

Programs

Maple

A187916 := proc(n)
    if type(n,'odd') then
        A000108(n);
    else
        A000108(n)-A000108(n/2);
    end if;
end proc:
seq(A187916(n),n=1..30) ; # R. J. Mathar, Jul 21 2015

Mathematica

Table[If[OddQ[n],CatalanNumber[n],CatalanNumber[n]-CatalanNumber[n/2]],{n,30}] (* Harvey P. Dale, May 22 2014 *)

Formula

Conjecture: -(n-2)*(n+2)*(n+1)*a(n) +8*(n+1)*(n^2-3*n+1)*a(n-1) +4*(-3*n^3+18*n^2-22*n+2)*a(n-2) -32*(n-2)*(n^2-3*n+1)*a(n-3) +16*

(2*n-7)*(n-3)*(2*n-3)*a(n-4)=0. - R. J. Mathar, Jul 21 2015