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A076005
Fifth column of triangle A075503.
3
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
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
Sequence in context: A223960 A351223 A156411 * A218503 A221620 A299954
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 02 2002
STATUS
approved