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A076010
Fourth column of triangle A075504.
3
1, 90, 5265, 255150, 11160261, 458810730, 18124795305, 697117731750, 26323112938221, 981154011007170, 36233774365169745, 1329174591745823550, 48521083977375207381, 1764912230785563088410, 64027726517340144702585
OFFSET
0,2
COMMENTS
The e.g.f. given below is Sum_{m=0..3} (A075513(4,m)*exp(9*(m+1)*x))/3!.
LINKS
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!.
MATHEMATICA
With[{m = 4}, Array[9^(# - m) StirlingS2[#, m] &, 15, m]] (* Michael De Vlieger, Dec 24 2017, after Indranil Ghosh at A075504 *)
CROSSREFS
Sequence in context: A111599 A111783 A075918 * A287021 A289308 A089513
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 02 2002
STATUS
approved