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

1, 104, 16192, 3745280, 1222291840, 537758144000, 307503360102400, 221965373351321600, 197530935371241472000, 212553938009841139712000, 272115940122123843665920000, 408828811133790954169303040000

Offset

2,2

Links

Table of n, a(n) for n=2..13.

Formula

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

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

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

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)).

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

Crossrefs

Cf. A091534, A091540.

Cf. A032031, A008544, A007559, A007661.

Sequence in context: A187700 A015272 A048920 * A157874 A282188 A271764

Adjacent sequences: A091536 A091537 A091538 * A091540 A091541 A091542

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 13 2004

Status

approved