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

1,3

Links

Table of n, a(n) for n=1..27.

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

Example

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

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 *)

Crossrefs

Cf. A000912, A000108

Sequence in context: A120779 A082189 A129795 * A052644 A052280 A195541

Adjacent sequences: A187913 A187914 A187915 * A187917 A187918 A187919

Keyword

nonn,easy

Author

Gary W. Adamson, Mar 15 2011

Status

approved