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 A079913 #30 Dec 03 2021 17:08:27
%S A079913 1,9,221,2227,15458,80196,334072,1173240,3598120,9856552,24553080,
%T A079913 56423032,121013800,244555560,469343992,860997880,1517994792,
%U A079913 2583928360,4262971000,6839066232,10699415080,16362861352,24513820920,36042440440,52091711272,74112304680
%N A079913 Solution to the Dancing School Problem with 8 girls and n+8 boys: f(8,n).
%C A079913 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 A079913 For fixed g, f(g,n) is polynomial in n for n >= g-2. See reference.
%H A079913 Colin Barker, <a href="/A079913/b079913.txt">Table of n, a(n) for n = 0..1000</a>
%H A079913 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 A079913 Jaap Spies, <a href="http://www.jaapspies.nl/mathfiles/dancingschool.pdf">Dancing School Problems, Permanent solutions of Problem 29</a>.
%H A079913 Jaap Spies, <a href="http://www.jaapspies.nl/oeis/a079913.sage">Sage program for computing A079913</a>.
%H A079913 Jaap Spies, <a href="http://www.jaapspies.nl/mathfiles/dancing.sage">Sage program for computing the polynomial a(n)</a>.
%H A079913 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 A079913 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A079913 a(0)=1, a(1)=9, a(2)=221, a(3)=2227, a(4)=15459, a(5)=80196, for n >= 6, a(n)= n^8 -20*n^7 +238*n^6 -1820*n^5 +9625*n^4 -35000*n^3 +84448*n^2 -122240*n +80680.
%F A079913 G.f.: -(484*x^14 -3902*x^13 +13791*x^12 -25930*x^11 +32928*x^10 -15756*x^9 +14443*x^8 +8652*x^7 +8524*x^6 +3690*x^5 +2741*x^4 +478*x^3 +176*x^2 +1) / (x -1)^9. - _Colin Barker_, Jan 05 2015
%F A079913 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9), for n>8. - _Wesley Ivan Hurt_, Sep 17 2015
%p A079913 A079913 := n->n^8 -20*n^7 +238*n^6 -1820*n^5 +9625*n^4 -35000*n^3 +84448*n^2 -122240*n +80680: (1,9,221,2227,15458,80196, seq(A079913(n), n=6..30)); # edited by _Wesley Ivan Hurt_, Sep 17 2015
%t A079913 CoefficientList[Series[-(484*x^14 - 3902*x^13 + 13791*x^12 - 25930*x^11 + 32928*x^10 - 15756*x^9 + 14443*x^8 + 8652*x^7 + 8524*x^6 + 3690*x^5 + 2741*x^4 + 478*x^3 + 176*x^2 + 1)/(x - 1)^9, {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Sep 17 2015 *)
%o A079913 (PARI) Vec(-(484*x^14 -3902*x^13 +13791*x^12 -25930*x^11 +32928*x^10 -15756*x^9 +14443*x^8 +8652*x^7 +8524*x^6 +3690*x^5 +2741*x^4 +478*x^3 +176*x^2 +1)/(x -1)^9 + O(x^100)) \\ _Colin Barker_, Jan 05 2015
%Y A079913 Cf. A079908-A079928.
%K A079913 nonn,easy
%O A079913 0,2
%A A079913 _Jaap Spies_, Jan 28 2003