a(n) = binomial coefficient C(n,44).

Terms

a(0) =1a(1) =45a(2) =1035a(3) =16215a(4) =194580a(5) =1906884a(6) =15890700a(7) =115775100a(8) =752538150a(9) =4431613550a(10) =23930713170a(11) =119653565850a(12) =558383307300