A091739 Third column (k=7) sequence of array A090216 ((5,5)-Stirling2) divided by 600.

1, 4440, 12715200, 33158592000, 84365452800000, 213181366579200000, 537634980016128000000, 1355141067314135040000000, 3415172150786516582400000000, 8606389816065144913920000000000

Offset: 0

Author

Wolfdieter Lang, Feb 13 2004

Keywords

• nonn
• easy

Crossrefs

Cf. A091553 (third column of array (4, 4)-Stirling2 divided by 72).

Formula

a(n)= A090216(n+2, 7)/600, n>=0.

a(n)= ((5!)^n)*(1-2*6^(n+1)+binomial(7, 2)^(n+1))/(2*5). From eq.12 of the Blasiak et al. reference given in A007840 with r=5=s, k=7.

a(n)= (21*(7*6*5*4*3)^n - 12*(6*5*4*3*2)^n + (5*4*3*2*1)^n)/10.

G.f.: (1+1080*x)/product(1-fallfac(p, 5)*x, p=5..7), with fallfac(n, m) := A008279(n, m) (falling factorials).