# Sum of products of binomials satisfies recurrence relation?

i need to know if the sequence $$(a_n)_{n \geq 0}$$ defined by $$a_n =\sum_{s=3n}^{16n} C_{15n}^{s-3n} \; C_{14n}^{s-2n} \; C_{12n+s}^{12n}$$ satisfies a recurrence relation ( type sequence Apery) or not.

i tried using Maple but it fail maybe my computer is not very strong for that.

i think intuitively but i'm not sure) that this sequence satisfy a recurrence relation with polynomial coefficient (as apery sequence) but may be the ordre of the recurrence is very high and the polynomial are very complicate, so please if someone has a strong computer and advanced Maple or Mathematica try to look the recurrence, if this doesn't function , i would like to know if Zeilberger algorithm can confirme the existence of such recurrence. thank you: my email is mamiladi@yahoo.com