OFFSET
0,2
COMMENTS
Hankel transform is A167423.
Apparently a(n) = A071716(n) if n>1. - R. J. Mathar, Nov 12 2009
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..500
Murray Tannock, Equivalence classes of mesh patterns with a dominating pattern, MSc Thesis, Reykjavik Univ., May 2016. See Appendix B2
FORMULA
a(n) = Sum_{k=0..n} A000108(k)*C(1,n-k).
a(0)= 1, a(n) = A005807(n-1) for n>0. - Philippe Deléham, Nov 25 2009
(n+1)*a(n) +(-3*n+1)*a(n-1) +2*(-2*n+5)*a(n-2)=0, for n>2. - R. J. Mathar, Feb 10 2015
-(n+1)*(5*n-6)*a(n) +2*(5*n-1)*(2*n-3)*a(n-1)=0. - R. J. Mathar, Feb 10 2015
The o.g.f. A(x) satisfies [x^n] A(x)^(5*n) = binomial(5*n,2*n) = A001450(n). Cf. A182959. - Peter Bala, Oct 04 2015
MAPLE
A167422List := proc(m) local A, P, n; A := [1, 2]; P := [1];
for n from 1 to m - 2 do P := ListTools:-PartialSums([op(P), A[-1]]);
A := [op(A), P[-1]] od; A end: A167422List(26); # Peter Luschny, Mar 24 2022
MATHEMATICA
Table[If[n < 2, n + 1, Binomial[2 n, n]/(n + 1) + Binomial[2 (n - 1), n - 1]/n], {n, 0, 25}] (* Michael De Vlieger, Oct 05 2015 *)
CoefficientList[Series[(1 + t)*(1 - Sqrt[1 - 4*t])/(2*t), {t, 0, 50}], t] (* G. C. Greubel, Jun 12 2016 *)
PROG
(PARI) a(n) = if (n<2, n+1, binomial(2*n, n)/(n+1) + binomial(2*(n-1), n-1)/n);
vector(50, n, a(n-1)) \\ Altug Alkan, Oct 04 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Nov 03 2009
STATUS
approved