A075925 Sixth column of triangle A075502.

1, 147, 13034, 907578, 54807627, 3016638009, 155726334148, 7676501248416, 365698066506773, 16976491006185711, 772549060467762942, 34614587429584922214, 1532054031119984651839, 67151990527665760714053

Offset: 0

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

Comments

The e.g.f. given below is Sum_{m=0..5} A075513(6,m)*exp(7*(m+1)*x)/5!.

Crossrefs

Cf. A075924, A076002.

Programs

Mathematica

CoefficientList[Series[1/Product[1-7k x,{k,6}],{x,0,20}],x] (* Harvey P. Dale, May 25 2012 *)

Formula

a(n) = A075502(n+6, 6) = (7^n)*S2(n+6, 6) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..5} A075513(6, m)*((m+1)*7)^n/5!.

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

E.g.f.: (d^6/dx^6)(((exp(7*x)-1)/7)^6)/6! = (-exp(7*x) + 160*exp(14*x) - 2430*exp(21*x) + 10240*exp(28*x) - 15625*exp(35*x) + 7776*exp(42*x))/5!.