|
%I #10 Dec 25 2017 04:01:22
%S 1,80,4160,179200,6967296,254607360,8940421120,305659904000,
%T 10259284361216,339910422691840,11158051230842880,363834840082022400,
%U 11805930580539867136,381715961976738283520,12309283295632755261440
%N Fourth column of triangle A075503.
%C The e.g.f. given below is Sum_{m=0..3} A075513(4,m)*exp(8*(m+1)*x)/3!.
%H Michael De Vlieger, <a href="/A076004/b076004.txt">Table of n, a(n) for n = 0..663</a>
%F a(n) = A075503(n+4, 4) = (8^n)*S2(n+4, 4) with S2(n, m) := A008277(n, m) (Stirling2).
%F a(n) = Sum_{m=0..3} ((A075513(4, m)*(m+1)*8)^n)/3!.
%F G.f.: 1/Product_{k=1..4} (1 - 8*k*x).
%F E.g.f.: (d^4/dx^4)(((exp(8*x)-1)/8)^4)/4! = (-exp(8*x) + 24*exp(16*x) - 81*exp(24*x) + 64*exp(32*x))/3!.
%t With[{m = 4}, Array[8^(# - m) StirlingS2[#, m] &, 15, m]] (* _Michael De Vlieger_, Dec 24 2017, after _Indranil Ghosh_ at A075503 *)
%Y Cf. A076003, A076005.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Oct 02 2002
|
