This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A051563 #11 Jul 07 2015 21:29:46 %S A051563 0,0,1,30,659,13145,255424,4985316,99236556,2030997852,42924478536, %T A051563 938984014584,21283428847680,500043968498880,12176238355176960, %U A051563 307176581692097280,8023946251816984320,216880826334455750400 %N A051563 Third unsigned column of triangle A051380. %C A051563 From _Johannes W. Meijer_, Oct 20 2009: (Start) %C A051563 The asymptotic expansion of the higher order exponential integral E(x,m=3,n=9) ~ exp(-x)/x^3*(1 - 30/x + 659/x^2 - 13145/x^3 + 255424/x^4 + ...) leads to the sequence given above. See A163931 and A163932 for more information. %C A051563 (End) %D A051563 Mitrinovic, D. S. and Mitrinovic, R. S. see reference given for triangle A051380. %F A051563 a(n) = A051380(n, 2)*(-1)^n; e.g.f.: ((log(1-x))^2)/(2*(1-x)^9). %F A051563 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,2,9)|, for n>=1. - _Milan Janjic_, Dec 21 2008 %Y A051563 Cf. A049389 (m=0), A051562 (m=1) unsigned columns. %K A051563 easy,nonn %O A051563 0,4 %A A051563 _Wolfdieter Lang_