OFFSET
1,1
FORMULA
a(n) = sum(i = 0..n+1, 2^i*binomial(n,n-i+1)*binomial(n+i-1,n-1))/n.
a(n) = T(2*n,n-1)/n where T(n,k) is triangle A116412.
D-finite with recurrence: (n+1)*a(n) +5*(-2*n+1)*a(n-1) +(n-2)*a(n-2)=0. a(n) = 2*A103210(n). - R. J. Mathar, May 23 2014
MAPLE
ogf := 1/x-4/(-sqrt(x^2-10*x+1)-x+1)-3;
series(ogf, x=0, 20): seq(coeff(%, x, n), n=0..19); # Peter Luschny, Mar 21 2014
PROG
(Maxima) a(n):=sum(2^i*binomial(n, n-i+1)*binomial(n+i-1, n-1), i, 0, n+1)/n;
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Mar 20 2014
STATUS
approved