A076007 - OEIS

%I #10 Dec 25 2017 04:01:35

%S 1,224,29568,3010560,262090752,20558512128,1498264109056,

%T 103450998210560,6857541631868928,440486826671603712,

%U 27603867324502769664,1696189816779885772800,102592999712419955605504

%N Seventh column of triangle A075503.

%C The e.g.f. given below is Sum_{m=0..6} (A075513(7,m)*exp(8*(m+1)*x))/6!.

%H Michael De Vlieger, <a href="/A076007/b076007.txt">Table of n, a(n) for n = 0..570</a>

%F a(n) = A075503(n+7, 7) = (8^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)*8)^n)/6!.

%F G.f.: 1/Product_{k=1..7} (1 - 8*k*x).

%F E.g.f.: (d^7/dx^7)(((exp(8*x)-1)/8)^7)/7! = (exp(8*x) - 384*exp(16*x) + 10935*exp(24*x) - 81920*exp(32*x) + 234375*exp(40*x) - 279936*exp(48*x) + 117649*exp(56*x))/6!.

%t With[{m = 7}, Array[8^(# - m) StirlingS2[#, m] &, 13, m]] (* _Michael De Vlieger_, Dec 24 2017, after _Indranil Ghosh_ at A075503 *)

%Y Cf. A076006.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Oct 02 2002