A075924 Fifth column of triangle A075502.

1, 105, 6860, 360150, 16689351, 714717675, 29027537770, 1135995214200, 43285014073301, 1617172212901245, 59536438207963080, 2167526889938878650, 78241359077417918851, 2805721220626405336815, 100098458195602131838790

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(7*(m+1)*x)/4!.

Crossrefs

Cf. A075923, A075925.

Formula

a(n) = A075502(n+5, 5) = (7^n)*S2(n+5, 5) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..4} A075513(5, m)*((m+1)*7)^n/4!.

G.f.: 1/Product_{k=1..5} (1 - 7*k*x).

E.g.f.: (d^5/dx^5)(((exp(7*x)-1)/7)^5)/5! = (exp(7*x) - 64*exp(14*x) + 486*exp(21*x) - 1024*exp(28*x) + 625*exp(35*x))/4!.