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%I #7 Jul 27 2022 08:47:36
%S 1,28,960,43200,2520000,186278400,17069875200,1902071808000,
%T 253487646720000,39833773056000000,7291173820170240000,
%U 1538106259064094720000,370502654756909875200000
%N Second column (k=3) sequence of array A078740 ((3,2)-Stirling2) divided by 6.
%F a(n)= n!*(n+1)!*(-3 + (n+2)*(n+1)/2)/(3!)^2, n>=2.
%F E.g.f.: (hypergeom([2, 3], [], x) - 3*hypergeom([1, 2], [], x) + 2)/(3!)^2.
%F a(n)=product(j+2, j=0..n-1)* (-3*product(j+1, j=0..n-1) + product(j+3, j=0..n-1))/(3!)^2, n>=2. From eq.12 of the Blasiak et al. reference given in A078740 with r=3, s=2, k=3.
%F D-finite with recurrence a(n) +(-n^2-7*n-24)*a(n-1) +12*(n^2+4*n+6)*a(n-2) -36*n*(n+1)*a(n-3)=0. - _R. J. Mathar_, Jul 27 2022
%p A091549 := proc(n)
%p n!*(n+1)!*(-3 + (n+2)*(n+1)/2)/(3!)^2 ;
%p end proc:
%p seq(A091549(n),n=2..30) ; # _R. J. Mathar_, Jul 27 2022
%K nonn,easy
%O 2,2
%A _Wolfdieter Lang_, Feb 13 2004