A091549 Second column (k=3) sequence of array A078740 ((3,2)-Stirling2) divided by 6.

1, 28, 960, 43200, 2520000, 186278400, 17069875200, 1902071808000, 253487646720000, 39833773056000000, 7291173820170240000, 1538106259064094720000, 370502654756909875200000

Offset

2,2

Links

Table of n, a(n) for n=2..14.

Formula

a(n)= n!*(n+1)!*(-3 + (n+2)*(n+1)/2)/(3!)^2, n>=2.

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

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.

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

Maple

A091549 := proc(n)
    n!*(n+1)!*(-3 + (n+2)*(n+1)/2)/(3!)^2 ;
end proc:
seq(A091549(n), n=2..30) ; # R. J. Mathar, Jul 27 2022

Crossrefs

Sequence in context: A239336 A203135 A097579 * A034904 A189995 A228689

Adjacent sequences: A091546 A091547 A091548 * A091550 A091551 A091552

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 13 2004

Status

approved