A076006 -id:A076006 - 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!.

A076007 Seventh column of triangle A075503.

Original entry on oeis.org

1, 224, 29568, 3010560, 262090752, 20558512128, 1498264109056, 103450998210560, 6857541631868928, 440486826671603712, 27603867324502769664, 1696189816779885772800, 102592999712419955605504

Offset: 0

Wolfdieter Lang, Oct 02 2002

The e.g.f. given below is Sum_{m=0..6} (A075513(7,m)*exp(8*(m+1)*x))/6!.

Michael De Vlieger, Table of n, a(n) for n = 0..570

Cf. A076006.

With[{m = 7}, Array[8^(# - m) StirlingS2[#, m] &, 13, m]] (* Michael De Vlieger, Dec 24 2017, after Indranil Ghosh at A075503 *)

a(n) = A075503(n+7, 7) = (8^n)*S2(n+7, 7) with S2(n, m) := A008277(n, m) (Stirling2).
a(n) = Sum_{m=0..6} (A075513(7, m)*((m+1)*8)^n)/6!.
G.f.: 1/Product_{k=1..7} (1 - 8*k*x).
E.g.f.: (d^7/dx^7)(((exp(8*x)-1)/8)^7)/7! = (exp(8*x) - 384*exp(16*x) + 10935*exp(24*x) - 81920*exp(32*x) + 234375*exp(40*x) - 279936*exp(48*x) + 117649*exp(56*x))/6!.

cp's OEIS Frontend

A076005 Fifth column of triangle A075503.

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