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A079915 Solution to the Dancing School Problem with 10 girls and n+10 boys: f(10,n).

%I A079915 #20 Dec 03 2021 17:08:59
%S A079915 1,11,596,9627,103129,780902,4557284,21670160,87396728,308055528,
%T A079915 971055240,2780440664,7324967640,17945144328,41249101928,89635336440,
%U A079915 185317652664,366517590440,696695849928
%N A079915 Solution to the Dancing School Problem with 10 girls and n+10 boys: f(10,n).
%C A079915 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 A079915 For fixed g, f(g,n) is polynomial in n for n >= g-2. See reference.
%D A079915 Jaap Spies, Dancing School Problems, Nieuw Archief voor Wiskunde 5/7 nr. 4, Dec 2006, pp. 283-285.
%H A079915 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 A079915 Jaap Spies, <a href="http://www.jaapspies.nl/mathfiles/dancingschool.pdf">Dancing School Problems, Permanent solutions of Problem 29</a>.
%H A079915 Jaap Spies, <a href="http://www.jaapspies.nl/oeis/a079915.sage">Sage program for computing A079915</a>.
%H A079915 Jaap Spies, <a href="http://www.jaapspies.nl/mathfiles/dancing.sage">Sage program for computing the polynomial a(n)</a>.
%H A079915 Jaap Spies, <a href="http://www.jaapspies.nl/bookb5.pdf">A Bit of Math, The Art of Problem Solving</a>, Jaap Spies Publishers (2019).
%F A079915 for n>=8: a(n) = n^10 -35*n^9 +675*n^8 -8610*n^7 +78435*n^6 -523467*n^5 +2562525*n^4 -9008160*n^3 +21623220*n^2 -31840760*n +21750840.
%p A079915 f:= n-> n^10 -35*n^9 +675*n^8 -8610*n^7 +78435*n^6 -523467*n^5 +2562525*n^4 -9008160*n^3 +21623220*n^2 -31840760*n +21750840: seq(f(i), i=8..21);
%Y A079915 Cf. A079908-A079928.
%K A079915 nonn
%O A079915 0,2
%A A079915 _Jaap Spies_, Jan 28 2003
%E A079915 Corrected by _Jaap Spies_, Feb 01 2004