A076013 Seventh column of triangle A075504.

1, 252, 37422, 4286520, 419818707, 37047106404, 3037410645984, 235940417032320, 17594974122819093, 1271468563282273356, 89638618747098243186, 6196581962116572990600, 421646012618644954061559

Offset: 0

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

Comments

The e.g.f. given below is Sum_{m=0..6} (A075513(7,m)*exp(9*(m+1)*x))/6!.

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..554

Crossrefs

Cf. A075504, A075513, A076012.

Programs

Mathematica

With[{m = 7}, Array[9^(# - m) StirlingS2[#, m] &, 13, m]] (* Michael De Vlieger, Dec 24 2017, after Indranil Ghosh at A075504 *)

Formula

a(n) = A075504(n+7, 7) = (9^n)*S2(n+7, 7) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..6} (A075513(7, m)*((m+1)*9)^n)/6!.

G.f.: 1/Product_{k=1..7} (1 - 9*k*x).

E.g.f.: (d^7/dx^7)(((exp(9*x)-1)/9)^7)/7! = (exp(9*x) - 384*exp(18*x) + 10935*exp(27*x) - 81920*exp(36*x) + 234375*exp(45*x) - 279936*exp(54*x) + 117649*exp(63*x))/6!.