A075516 Sixth column of triangle A075498.

1, 63, 2394, 71442, 1848987, 43615341, 964942308, 20385709344, 416206043253, 8280505692459, 161494678323342, 3101091077181006, 58823743379417199, 1104995938593100617, 20595841868175915096

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(3*(m+1)*x)/5!.

Crossrefs

Cf. A008277, A075498, A075513, A075515, A075906.

Formula

a(n) = A075498(n+6, 6) = (3^n)*S2(n+6, 6) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..5} A075513(6, m)*((m+1)*3)^n/5!.

G.f.: 1/Product_{k=1..6} (1 - 3*k*x).

E.g.f.: (d^6/dx^6)(((exp(3*x)-1)/3)^6)/6! = (-exp(3*x) + 160*exp(6*x) - 2430*exp(9*x) + 10240*exp(12*x) - 15625*exp(15*x) + 7776*exp(18*x))/5!.