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Seventh column of triangle A075504.
4

%I #10 Dec 25 2017 04:01:55

%S 1,252,37422,4286520,419818707,37047106404,3037410645984,

%T 235940417032320,17594974122819093,1271468563282273356,

%U 89638618747098243186,6196581962116572990600,421646012618644954061559

%N Seventh column of triangle A075504.

%C The e.g.f. given below is Sum_{m=0..6} (A075513(7,m)*exp(9*(m+1)*x))/6!.

%H Michael De Vlieger, <a href="/A076013/b076013.txt">Table of n, a(n) for n = 0..554</a>

%F a(n) = A075504(n+7, 7) = (9^n)*S2(n+7, 7) with S2(n, m) := A008277(n, m) (Stirling2).

%F a(n) = Sum_{m=0..6} (A075513(7, m)*((m+1)*9)^n)/6!.

%F G.f.: 1/Product_{k=1..7} (1 - 9*k*x).

%F E.g.f.: (d^7/dx^7)(((exp(9*x)-1)/9)^7)/7! = (exp(9*x) - 384*exp(18*x) + 10935*exp(27*x) - 81920*exp(36*x) + 234375*exp(45*x) - 279936*exp(54*x) + 117649*exp(63*x))/6!.

%t With[{m = 7}, Array[9^(# - m) StirlingS2[#, m] &, 13, m]] (* _Michael De Vlieger_, Dec 24 2017, after _Indranil Ghosh_ at A075504 *)

%Y Cf. A076012.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Oct 02 2002