OFFSET
0,2
FORMULA
a(n) = sum((-1)^(n-k)*binomial(n,k)*binomial(2*k,k)*binomial(3*k,k),k=0..n).
D-finite with recurrence Recurrence: (n+3)^2*a(n+3)-(24*n^2+120*n+149)*a(n+2)-51*(n+2)^2*a(n+1)-26*(n+1)*(n+2)*a(n)=0.
E.g.f.: exp(-x)*F(1/3,2/3;1,1;27*x), where F(a1,a2;b1;z) is a hypergeometric series.
a(n) ~ 13*sqrt(3) * 26^n / (27*Pi*n). - Vaclav Kotesovec, Mar 02 2014
MATHEMATICA
Table[Sum[Binomial[n, k]Binomial[2k, k]Binomial[3k, k](-1)^(n-k), {k, 0, n}], {n, 0, 16}]
PROG
(Maxima) makelist(sum((-1)^(n-k)*binomial(n, k)*binomial(2*k, k)*binomial(3*k, k), k, 0, n), n, 0, 16);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, Apr 14 2011
STATUS
approved