A075917 Fourth column of triangle A075501.

1, 60, 2340, 75600, 2204496, 60419520, 1591202880, 40800672000, 1027086863616, 25522067450880, 628349082117120, 15366613964083200, 373968813041012736, 9068526888588656640, 219326169845571010560

Offset: 0

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

Comments

The e.g.f. given below is Sum_{m=0..3} A075513(4,m)*exp(6*(m+1)*x)/3!.

Crossrefs

Cf. A075916, A075918.

Formula

a(n) = A075501(n+4, 4) = (6^n)*S2(n+4, 4) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..3} A075513(4, m)*((m+1)*6)^n/3!.

G.f.: 1/Product_{k=1..4} (1 - 6*k*x).

E.g.f.: (d^4/dx^4)(((exp(6*x)-1)/6)^4)/4! = (-exp(6*x) + 24*exp(12*x) - 81*exp(18*x) + 64*exp(24*x))/3!.