A051546 - OEIS

%I #11 Jul 07 2015 21:27:10

%S 0,0,1,24,431,7155,117454,1961470,33775244,603682596,11235811536,

%T 218055250512,4413843664416,93156324734304,2048591287486080,

%U 46898664421553280,1116592842912341760,27618683992928743680

%N Third unsigned column of triangle A051339.

%C From _Johannes W. Meijer_, Oct 20 2009: (Start)

%C The asymptotic expansion of the higher order exponential integral E(x,m=3,n=7) ~ exp(-x)/x^3*(1 - 24/x + 431/x^2 - 7155/x^3 + 117454/x^4 + ...) leads to the sequence given above. See A163931 and A163932 for more information.

%C (End)

%D Mitrinovic, D. S. and Mitrinovic, R. S. see reference given for triangle A051339.

%F a(n) = A051339(n, 2)*(-1)^n; e.g.f.: (log(1-x))^2/(2*(1-x)^7).

%F If we define f(n,i,a)=sum(binomial(n,k)*stirling1(n-k,i)*product(-a-j,j=0..k-1),k=0..n-i), then a(n) = |f(n,2,7)|, for n>=1. - _Milan Janjic_, Dec 21 2008

%Y Cf. A001730 (m=0), A051545 (m=1) unsigned columns.

%K easy,nonn

%O 0,4

%A _Wolfdieter Lang_