OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
FORMULA
G.f.: 1/((3*g-1)*(g^3-2*g^2+g-1)*(g-1)^2) where g*(1-g)^2 = x. - Mark van Hoeij, Nov 10 2011
Recurrence: 2*n*(2*n-1)*a(n) = (31*n^2-29*n+6)*a(n-1) - 3*(3*n-2)*(3*n-1)*a(n-2). - Vaclav Kotesovec, Oct 14 2012
a(n) ~ 3^(3*n+5/2)/(23*2^(2*n+1)*sqrt(Pi)*sqrt(n)). - Vaclav Kotesovec, Oct 14 2012
a(n) = Sum_{k=1..n} binomial(3*k-1,k-1). [Bruno Berselli, Oct 10 2015]
MATHEMATICA
Table[Sum[Binomial[3*k, k]/3, {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Oct 14 2012 *)
PROG
(PARI) a(n)=sum(k=1, n, binomial(3*k, k))/3 \\ Charles R Greathouse IV, Nov 10 2011
(PARI) a=vector(99, i, 1); for(n=2, #a, a[n]=a[n-1]+binomial(3*n, n)/3); a \\ Charles R Greathouse IV, Nov 10 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Oct 21 2003
STATUS
approved