A075919 - OEIS

%I #8 Dec 27 2017 01:33:16

%S 1,126,9576,571536,29583792,1395690912,61756307712,2609370796032,

%T 106548747072768,4239618914539008,165370550603102208,

%U 6351034526066700288,240942052882092847104,9052126728954680254464

%N Sixth column of triangle A075501.

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

%F a(n) = A075501(n+6, 6) = (6^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)*6)^n/5!.

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

%F E.g.f.: (d^6/dx^6)(((exp(6*x)-1)/6)^6)/6! = (-exp(6*x) + 160*exp(12*x) - 2430*exp(18*x) + 10240*exp(24*x) - 15625*exp(30*x) + 7776*exp(36*x))/5!.

%Y Cf. A075918, A075920.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Oct 02 2002