A076012 - OEIS

%I #10 Dec 25 2017 04:01:52

%S 1,189,21546,1928934,149767947,10598527863,703442942532,

%T 44583546335328,2730727849782933,162985193544670497,

%U 9536099260315021758,549348981049383669882,31261349005300855653759

%N Sixth column of triangle A075504.

%C The e.g.f. given below is Sum_{m=0..5} (A075513(6,m)*exp(9*(m+1)*x))/5!.

%H Michael De Vlieger, <a href="/A076012/b076012.txt">Table of n, a(n) for n = 0..576</a>

%F a(n) = A075504(n+6, 6) = (9^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)*9)^n)/5!.

%F G.f.: 1/Product_{k=1..6} (1 - 9*k*x).

%F E.g.f.: (d^6/dx^6)(((exp(9*x)-1)/9)^6)/6! = (-exp(9*x) + 160*exp(18*x) - 2430*exp(27*x) + 10240*exp(36*x) - 15625*exp(45*x) + 7776*exp(54*x))/5!.

%t With[{m = 6}, Array[9^(# - m) StirlingS2[#, m] &, 13, m]] (* _Michael De Vlieger_, Dec 24 2017, after _Indranil Ghosh_ at A075504 *)

%Y Cf. A076011, A076013.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Oct 02 2002