A076010 Fourth column of triangle A075504.

1, 90, 5265, 255150, 11160261, 458810730, 18124795305, 697117731750, 26323112938221, 981154011007170, 36233774365169745, 1329174591745823550, 48521083977375207381, 1764912230785563088410, 64027726517340144702585

Offset: 0

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

Comments

The e.g.f. given below is Sum_{m=0..3} (A075513(4,m)*exp(9*(m+1)*x))/3!.

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..641

Crossrefs

Cf. A076009, A076011.

Programs

Mathematica

With[{m = 4}, Array[9^(# - m) StirlingS2[#, m] &, 15, m]] (* Michael De Vlieger, Dec 24 2017, after Indranil Ghosh at A075504 *)

Formula

a(n) = A075504(n+4, 4) = (9^n)*S2(n+4, 4) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = (-9^n + 24*18^n - 81*27^n + 64*36^n)/3!.

G.f.: 1/Product_{k=1..4} (1 - 9*k*x).

E.g.f.: (d^4/dx^4)(((exp(9*x)-1)/9)^4)/4! = (-exp(9*x) + 24*exp(18*x) - 81*exp(27*x) + 64*exp(36*x))/3!.