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A075925 Sixth column of triangle A075502. 3

%I

%S 1,147,13034,907578,54807627,3016638009,155726334148,7676501248416,

%T 365698066506773,16976491006185711,772549060467762942,

%U 34614587429584922214,1532054031119984651839,67151990527665760714053

%N Sixth column of triangle A075502.

%C The e.g.f. given below is Sum_{m=0..5} A075513(6,m)*exp(7*(m+1)*x)/5!.

%F a(n) = A075502(n+6, 6) = (7^n)*S2(n+6, 6) with S2(n, m) := A008277(n, m) (Stirling2).

%F a(n) = Sum_{m=0..5} A075513(6, m)*((m+1)*7)^n/5!.

%F G.f.: 1/Product_{k=1..6} (1 - 7*k*x).

%F E.g.f.: (d^6/dx^6)(((exp(7*x)-1)/7)^6)/6! = (-exp(7*x) + 160*exp(14*x) - 2430*exp(21*x) + 10240*exp(28*x) - 15625*exp(35*x) + 7776*exp(42*x))/5!.

%t CoefficientList[Series[1/Product[1-7k x,{k,6}],{x,0,20}],x] (* _Harvey P. Dale_, May 25 2012 *)

%Y Cf. A075924, A076002.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Oct 02 2002

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Last modified August 6 08:22 EDT 2020. Contains 336228 sequences. (Running on oeis4.)