A076005 Fifth column of triangle A075503.

1, 120, 8960, 537600, 28471296, 1393459200, 64678789120, 2892811468800, 125971743113216, 5378780147220480, 226309257119662080, 9416205124868505600, 388454135575280091136, 15919881384987941928960

Offset

0,2

Comments

The e.g.f. given below is Sum_{m=0..4} A075513(5,m)*exp(8*(m+1)*x)/4!.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..623

Formula

a(n) = A075503(n+5, 5) = (8^n)*S2(n+5, 5) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = Sum_{m=0..4} (A075513(5, m)*((m+1)*8)^n)/4!.

G.f.: 1/Product_{k=1..5} (1 - 8*k*x).

E.g.f.: (d^5/dx^5)(((exp(8*x)-1)/8)^5)/5! = (exp(8*x) - 64*exp(16*x) + 486*exp(24*x) - 1024*exp(32*x) + 625*exp(40*x))/4!.

Mathematica

With[{m = 5}, Array[8^(# - m) StirlingS2[#, m] &, 14, m]] (* Michael De Vlieger, Dec 24 2017, after Indranil Ghosh at A075503 *)

Crossrefs

Cf. A076004, A076006.

Sequence in context: A223960 A351223 A156411 * A218503 A221620 A299954

Adjacent sequences: A076002 A076003 A076004 * A076006 A076007 A076008

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 02 2002

Status

approved