A076009 Third column of triangle A075504.

1, 54, 2025, 65610, 1974861, 57041334, 1607609025, 44625100770, 1226874595221, 33521945231214, 912229968911625, 24758714599712730, 670798674525559581, 18153207600055622694, 490886209059873519825

Offset: 0

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

Comments

The e.g.f. given below is Sum_{m=0..2} (A075513(3,m)*exp(9*(m+1)*x))/2!.

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..698

Crossrefs

Cf. A076008, A076010.

Programs

Mathematica

With[{m = 3}, Array[9^(# - m) StirlingS2[#, m] &, 15, m]] (* Michael De Vlieger, Dec 24 2017, after Indranil Ghosh at A075504 *)

Formula

a(n) = A075504(n+3, 3) = (9^n)*S2(n+3, 3) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = (9^n - 8*18^n + 9*27^n)/2.

G.f.: 1/Product_{k=1..3} (1 - 9*k*x).

E.g.f.: (d^3/dx^3)(((exp(9*x)-1)/9)^3)/3! = (exp(9*x) - 8*exp(18*x) + 9*exp(27*x))/2!.