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A091539 Second column (k=3) of array A091534 ((5,2)-Stirling2) divided by 10. 3


%S 1,104,16192,3745280,1222291840,537758144000,307503360102400,

%T 221965373351321600,197530935371241472000,212553938009841139712000,

%U 272115940122123843665920000,408828811133790954169303040000

%N Second column (k=3) of array A091534 ((5,2)-Stirling2) divided by 10.

%F a(n)= A091534(n, 3)/10, n>=2.

%F a(n)= product(3*j+2, j=0..n-1)*(product(3*(j+1), j=0..n-1) - 3*product(3*j+1, j=0..n-1))/(3!*10). From eq.(12) of the Blasiak et reference(see A091534) for r=5, s=2 and k=3.

%F a(n)= (3^(2*n))*risefac(2/3, n)*(n!-3*risefac(1/3, n))/(3!*10), with risefac(x, n)=pochhammer(x, n).

%F a(n)= (fac3(3*n-1)/10)*(fac3(3*n) - 3*fac3(3*n-2))/3!, with fac3(3*n) := A032031(n)= n!*3^n, fac3(3*n-1) := A008544(n) and fac3(3*n-2)=A007559(n) (triple factorials: fac3(n)=A007661(n)).

%F E.g.f.: (hypergeom([2/3, 1], [], 9*x)-3*hypergeom([1/3, 2/3], [], 9*x)+2)/(3!*10).

%Y Cf. A091540.

%K nonn,easy

%O 2,2

%A _Wolfdieter Lang_, Feb 13 2004

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Last modified April 6 21:24 EDT 2020. Contains 333286 sequences. (Running on oeis4.)