A091553 Third column (k=6) sequence of array A090214 ((4,4)-Stirling2) divided by 72.

1, 704, 300096, 113762304, 41644855296, 15075073327104, 5436979231850496, 1958506906364411904, 705205813266345885696, 253891292037560301256704, 91402929045514567230160896, 32905302125838589613523861504

Offset: 0

Author

Wolfdieter Lang, Feb 13 2004

Keywords

• nonn
• easy

Crossrefs

Cf. A089518 (third column of array (3, 3)-Stirling2 divided by 9).

Formula

a(n)= A090214(n+2, 6)/72, n>=0.

a(n)= (15*(6*5*4*3)^n - 10*(5*4*3*2)^n + (4*3*2*1)^n)/3!.

G.f.: (1+200*x)/product(1-fallfac(p, 4)*x, p=4..6), with fallfac(n, m) := A008279(n, m) (falling factorials).

a(n)= ((4!)^n)*(1-2*5^(n+1)+binomial(6, 2)^(n+1))/3!. From eq.12 of the Blasiak et al. reference given in A078740 with r=4=s, k=6.