A075920 Seventh column of triangle A075501.

1, 168, 16632, 1270080, 82927152, 4878631296, 266658822144, 13809041326080, 686528482768128, 33073815190800384, 1554470788616718336, 71638807647968870400, 3249771974096785403904, 145542549641019667218432

Offset: 0

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

Comments

The e.g.f. given below is Sum_{m=0..6} A075513(7,m)exp(6*(m+1)*x)/6!.

Crossrefs

Cf. A075919.

Formula

a(n) = A075501(n+7, 7) = (6^n)S2(n+7, 7) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..6} A075513(7, m)*((m+1)*6)^n/6!.

G.f.: 1/Product_{k=1..7} (1 - 6*k*x).

E.g.f.: (d^7/dx^7)(((exp(6*x)-1)/6)^7)/7! = (exp(6*x) - 384*exp(12*x) + 10935*exp(18*x) - 81920*exp(24*x) + 234375*exp(30x) - 279936*exp(36*x) + 117649*exp(42*x))/6!.