A076004 -id:A076004 - cp's OEIS frontend

A076005 Fifth column of triangle A075503.

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

Offset: 0

Wolfdieter Lang, Oct 02 2002

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

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

Cf. A076004, A076006.

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

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!.

A076003 Third column of triangle A075503.

Original entry on oeis.org

1, 48, 1600, 46080, 1232896, 31653888, 792985600, 19566428160, 478167433216, 11613323132928, 280917704704000, 6777200695050240, 163215697915150336, 3926183399462535168, 94372512377130188800

Offset: 0

Wolfdieter Lang, Oct 02 2002

The e.g.f. given below is Sum_{m=0..2} A075513(3,m)*exp(8*(m+1)*x)/2!.

Cf. A060195, A076004.

a(n) = A075503(n+3, 3) = (8^n)*S2(n+3, 3) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = (8^n - 8*16^n + 9*24^n)/2.
G.f.: 1/Product_{k=1..3} (1 - 8*k*x).
E.g.f.: (d^3/dx^3)(((exp(8*x)-1)/8)^3)/3! = (exp(8*x) - 8*exp(16*x) + 9*exp(24*x))/2!.

cp's OEIS Frontend

A076005 Fifth column of triangle A075503.

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