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A091539 Second column (k=3) of array A091534 ((5,2)-Stirling2) divided by 10. 3
1, 104, 16192, 3745280, 1222291840, 537758144000, 307503360102400, 221965373351321600, 197530935371241472000, 212553938009841139712000, 272115940122123843665920000, 408828811133790954169303040000 (list; graph; refs; listen; history; text; internal format)
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(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.

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. A091540.

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

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Last modified February 25 08:48 EST 2020. Contains 332221 sequences. (Running on oeis4.)