OFFSET
0,2
COMMENTS
Coefficients of orthogonal polynomials.
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..150
H. E. Salzer, Orthogonal polynomials arising in the evaluation of inverse Laplace transforms, Math. Comp. 9 (1955), 164-177.
H. E. Salzer, Orthogonal polynomials arising in the evaluation of inverse Laplace transforms, Math. Comp. 9 (1955), 164-177. [Annotated scanned copy]
FORMULA
E.g.f.: (1-x)/(1-4*x)^(5/2).
Conjecture: a(n) +4*(-n-1)*a(n-1) +4*(-2*n+1)*a(n-2)=0. - R. J. Mathar, Jun 07 2013
MAPLE
with(combstruct): a:=n-> add((count(Permutation(n*2+1), size=n+1)), j=0..n+1)/2: seq(a(n), n=0..16); # Zerinvary Lajos, May 03 2007
MATHEMATICA
Join[{1}, Table[(n+2)(2n+1)(2n-1)!/(n-1)!, {n, 15}]] (* Harvey P. Dale, Jun 09 2011 *)
PROG
(PARI) a(n)=(n+2)*(2*n+1)*(2*n-1)!/(n-1)!
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
Edited by Ralf Stephan, Mar 21 2004
STATUS
approved