A075918 Fifth column of triangle A075501.

1, 90, 5040, 226800, 9008496, 330674400, 11511434880, 386143718400, 12611398415616, 403864019919360, 12744269679697920, 397694704355020800, 12304809943691636736, 378212825199337758720, 11565710925825703772160

Offset: 0

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

Comments

The e.g.f. given below is Sum_{m=0..4} A075513(5,m)*exp(6*(m+1)*x)/4!.

Crossrefs

Cf. A075917, A075919.

Formula

a(n) = A075501(n+5, 5) = (6^n)*S2(n+5, 5) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..4} A075513(5, m)*((m+1)*6)^n/4!.

G.f.: 1/Product_{k=1..5} (1 - 6*k*x).

E.g.f.: (d^5/dx^5)(((exp(6*x)-1)/6)^5)/5! = (exp(6*x) - 64*exp(12*x) + 486*exp(18*x) - 1024*exp(24*x) + 625*exp(30*x))/4!.