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 A079914 #24 Dec 03 2021 17:08:52
%S A079914 1,10,364,4664,40296,253072,1249768,5112544,17990600,56010096,
%T A079914 157175032,403579328,959942664,2136701200,4488418616,8961185952,
%U A079914 17105944648,31378295984,55549351800,95256535936,158727963272,257719103568
%N A079914 Solution to the Dancing School Problem with 9 girls and n+9 boys: f(9,n).
%C A079914 f(g,h) = per(B), the permanent of the (0,1)-matrix B of size g X g+h with b(i,j)=1 if and only if i <= j <= i+h. See A079908 for more information.
%C A079914 For fixed g, f(g,n) is polynomial in n for n >= g-2. See reference.
%H A079914 Colin Barker, <a href="/A079914/b079914.txt">Table of n, a(n) for n = 0..1000</a>
%H A079914 Jaap Spies, <a href="http://www.nieuwarchief.nl/serie5/pdf/naw5-2006-07-4-283.pdf">Dancing School Problems</a>, Nieuw Archief voor Wiskunde 5/7 nr. 4, Dec 2006, pp. 283-285.
%H A079914 Jaap Spies, <a href="http://www.jaapspies.nl/mathfiles/dancingschool.pdf">Dancing School Problems, Permanent solutions of Problem 29</a>.
%H A079914 Jaap Spies, <a href="http://www.jaapspies.nl/oeis/a079914.sage">Sage program for computing A079914</a>.
%H A079914 Jaap Spies, <a href="http://www.jaapspies.nl/mathfiles/dancing.sage">Sage program for computing the polynomial a(n)</a>.
%H A079914 Jaap Spies, <a href="http://www.jaapspies.nl/bookb5.pdf">A Bit of Math, The Art of Problem Solving</a>, Jaap Spies Publishers (2019).
%H A079914 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F A079914 a(0)=1, a(1)=10, a(2)=364, a(3)=4664, a(4)=40296, a(5)=253072, a(6)=1249768, for n >= 7: a(n)=n^9-27n^8+414n^7-4158n^6+29421n^5-148743n^4+530796n^3-1276992n^2+1866384n-1255608.
%F A079914 G.f.: -(5840*x^16 -52960*x^15 +210480*x^14 -481464*x^13 +671100*x^12 -619882*x^11 +258311*x^10 -123144*x^9 -98197*x^8 -57276*x^7 -46818*x^6 -18160*x^5 -9046*x^4 -1354*x^3 -309*x^2 -1) / (x -1)^10.- _Colin Barker_, Jan 05 2015
%p A079914 f := n->n^9-27*n^8+414*n^7-4158*n^6+29421*n^5-148743*n^4+530796*n^3-1276992*n^2+1866384*n-1255608; seq(f(i),i=7..21);
%t A079914 CoefficientList[Series[-(5840 x^16 - 52960 x^15 + 210480 x^14 - 481464 x^13 + 671100 x^12 - 619882 x^11 + 258311 x^10 - 123144 x^9 - 98197 x^8 - 57276 x^7 - 46818 x^6 - 18160 x^5 - 9046 x^4 - 1354 x^3 - 309 x^2 - 1)/(x - 1)^10, {x, 0, 21}], x] (* _Michael De Vlieger_, Dec 23 2019 *)
%o A079914 (PARI) Vec(-(5840*x^16 -52960*x^15 +210480*x^14 -481464*x^13 +671100*x^12 -619882*x^11 +258311*x^10 -123144*x^9 -98197*x^8 -57276*x^7 -46818*x^6 -18160*x^5 -9046*x^4 -1354*x^3 -309*x^2 -1) / (x -1)^10 + O(x^100)) \\ _Colin Barker_, Jan 05 2015
%Y A079914 Cf. A079908-A079928.
%K A079914 nonn,easy
%O A079914 0,2
%A A079914 _Jaap Spies_, Jan 28 2003