A076012 Sixth column of triangle A075504.

1, 189, 21546, 1928934, 149767947, 10598527863, 703442942532, 44583546335328, 2730727849782933, 162985193544670497, 9536099260315021758, 549348981049383669882, 31261349005300855653759

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

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..576

Crossrefs

Cf. A076011, A076013.

Programs

Mathematica

With[{m = 6}, Array[9^(# - m) StirlingS2[#, m] &, 13, m]] (* Michael De Vlieger, Dec 24 2017, after Indranil Ghosh at A075504 *)

Formula

a(n) = A075504(n+6, 6) = (9^n)*S2(n+6, 6) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..5} (A075513(6, m)*((m+1)*9)^n)/5!.

G.f.: 1/Product_{k=1..6} (1 - 9*k*x).

E.g.f.: (d^6/dx^6)(((exp(9*x)-1)/9)^6)/6! = (-exp(9*x) + 160*exp(18*x) - 2430*exp(27*x) + 10240*exp(36*x) - 15625*exp(45*x) + 7776*exp(54*x))/5!.