A076011 Fifth column of triangle A075504.

1, 135, 11340, 765450, 45605511, 2511058725, 131122437930, 6597627438600, 323216347675221, 15525889656392115, 734898808902814920, 34399620992372494950, 1596504028634137480131, 73607593519321749694305

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

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..604

Crossrefs

Cf. A076010, A076012.

Programs

Mathematica

With[{m = 5}, Array[9^(# - m) StirlingS2[#, m] &, 14, m]] (* Michael De Vlieger, Dec 24 2017, after Indranil Ghosh at A075504 *)

Formula

a(n) = A075504(n+5, 5) = (9^n)*S2(n+5, 5) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..4} (A075513(5, m)*(9*(m+1))^n)/4!.

G.f.: 1/Product_{k=1..5} (1 - 9*k*x).

E.g.f.: (d^5/dx^5)(((exp(9*x)-1)/9)^5)/5! = (exp(9*x) - 64*exp(18*x) + 486*exp(27*x) - 1024*exp(36*x) + 625*exp(45*x))/4!.