OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(n) = sum(C(i),i=n..2*n), where the C(n)'s are the Catalan numbers.
Recurrence: a(n+1)=a(n)+C(2n+2)+C(2n+1)-C(n).
Recurrence: (n-1)*n*(2*n+1)*(10*n^3 - 51*n^2 + 86*n - 49)*a(n) = 3*(n-1)*(140*n^5 - 844*n^4 + 1851*n^3 - 1784*n^2 + 701*n - 70)*a(n-1) - 6*(280*n^6 - 2308*n^5 + 7496*n^4 - 12166*n^3 + 10376*n^2 - 4523*n + 875)*a(n-2) + 4*(2*n-5)*(4*n-9)*(4*n-7)*(10*n^3 - 21*n^2 + 14*n - 4)*a(n-3). - Vaclav Kotesovec, Aug 13 2013
a(n) ~ 16^n/(3*sqrt(Pi/2)*n^(3/2)). - Vaclav Kotesovec, Aug 13 2013
MATHEMATICA
Table[Sum[Binomial[2i, i]/(i+1), {i, n, 2n}], {n, 0, 100}]
PROG
(Maxima) makelist(sum(binomial(2*i, i)/(i+1), i, n, 2*n), n, 0, 12);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Mar 28 2012
STATUS
approved