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Seventh column of triangle A075502.
3

%I #8 Dec 27 2017 01:34:46

%S 1,196,22638,2016840,153632787,10544644572,672413918176,

%T 40624783239040,2356312445219733,132435800821952628,

%U 7261903300743441714,390447849166013566200,20663998640254649395639

%N Seventh column of triangle A075502.

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

%F a(n) = A075502(n+7, 7) = (7^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)*7)^n/6!.

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

%F E.g.f.: (d^7/dx^7)(((exp(7*x)-1)/7)^7)/7! = (exp(7*x) - 384*exp(14*x) + 10935*exp(21*x) - 81920*exp(28*x) + 234375*exp(35*x) - 279936*exp(42*x) + 117649*exp(49*x))/6!.

%Y Cf. A075525.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Oct 02 2002