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A187916
a(n) = C(n) if n is odd, else C(n) - C(n/2); C(n) are Catalan numbers.
1
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
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
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Mar 15 2011
STATUS
approved