%I A073767
%S A073767 1,3,20,188,2214,30922,495816,8931960,177999366,3878476418,91558971096,
%T A073767 2324529942088,63084714688540,1820757355281828,55645592361311504,
%U A073767 1794034726184859120,60817844748284215110,2161623389394872099250
%N A073767 Bateman polynomial values n!Z_n(-1).
%D A073767 M. C. Fasenmyer, A note on pure recurrence relations, Amer. Math. Monthly 
               56, (1949), 14-17. Math. Rev. 10,704b.
%F A073767 a(n)=n!(Sum k=0..n (n+k)!/(k!^3(n-k)!)) = n!F(-n, n+1;1, 1;-1).
%F A073767 n(2n-3)a(n)=(2n-1)(3n^2-2n-4)a(n-1)-(2n-3)(3n^2-10n+4)(n-1)a(n-2)+(n-1)(2n-1)(n-2)^3a(n-3).
%o A073767 (PARI) a(n)=if(n<0,0,n!*sum(k=0,n,(n+k)!/(n-k)!/k!^3))
%Y A073767 Cf. A073768.
%Y A073767 Sequence in context: A129840 A085390 A065980 this_sequence A108206 A120485 
               A087152
%Y A073767 Adjacent sequences: A073764 A073765 A073766 this_sequence A073768 A073769 
               A073770
%K A073767 nonn
%O A073767 0,2
%A A073767 Michael Somos, Aug 08 2002