OFFSET
0,4
COMMENTS
The binomial transform of a(n) are the complementary Riordan numbers A194589 (see link).
LINKS
Peter Luschny, The lost Catalan numbers
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*cr(k), where cr(k) are the complementary Riordan numbers A194589.
MAPLE
MATHEMATICA
sf[n_] := n!/Quotient[n, 2]!^2;
a[n_] := (-1)^n (sf[n + 1] * If[EvenQ[n], 1, (n + 1)/2] - 2^n)/2;
Table[a[n], {n, 0, 32}] (* Jean-François Alcover, Jun 26 2019 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, Aug 30 2011
STATUS
approved