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 A089277 #23 Jul 08 2025 11:03:58
%S A089277 1,112,7896,453056,23232176,1113673728,51155215360,2284897159168,
%T A089277 100157064553728,4334351404617728,185915811851773952,
%U A089277 7925465707325177856,336395829865869340672,14234737653310804590592
%N A089277 Sixth column of the triangle A071951 (Legendre-Stirling).
%H A089277 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (112,-4648,89280,-808848,3110400,-3628800).
%F A089277 G.f.: 1/Product_{p=1..6} (1 - p*(p+1)*x) = 1/((1-2*x)*(1-6*x)*(1-12*x)*(1-20*x)*(1-30*x)*(1-42*x)).
%F A089277 a(n) = A071951(n+6, 6), n>=0.
%F A089277 a(n) = (Sum_{p=1..6} A089278(6, p)*(p*(p+1))^n)/A089500(6) = (-11*2^n + 7425*6^n - 266112*12^n + 2000000*20^n - 4640625*30^n + 3176523*42^n)/277200.
%F A089277 a(n) = det(|ps(i+6,j+5)|, 1 <= i,j <= n), where ps(n,k) are Legendre-Stirling numbers of the first kind (A129467). - _Mircea Merca_, Apr 06 2013
%Y A089277 Cf. A071951, A071952, A089274, A089278, A089500, A129467.
%K A089277 nonn,easy
%O A089277 0,2
%A A089277 _Wolfdieter Lang_, Nov 07 2003