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%I #10 Jul 19 2020 07:22:18
%S 0,784,73200,3884640,182107936,8277726192,373396825488,16812327355840,
%T 756652360885056,34050346486482384,1532275508306401840,
%U 68952496159266606624,3102863293076011859040,139628857613659024861360,6283298684030318768507856,282748441663401954476011392
%N Number of permutations of 8 indistinguishable copies of 1..n with exactly 2 adjacent element pairs in decreasing order.
%H Andrew Howroyd, <a href="/A151658/b151658.txt">Table of n, a(n) for n = 1..500</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (66,-1083,6508,-13671,11826,-3645).
%F a(n) = 45^n - (8*n + 1)*9^n + 4*n*(8*n + 1). - _Andrew Howroyd_, May 06 2020
%F From _Colin Barker_, Jul 19 2020: (Start)
%F G.f.: 16*x^2*(49 + 1341*x - 6093*x^2 - 6561*x^3) / ((1 - x)^3*(1 - 9*x)^2*(1 - 45*x)).
%F a(n) = 66*a(n-1) - 1083*a(n-2) + 6508*a(n-3) - 13671*a(n-4) + 11826*a(n-5) - 3645*a(n-6) for n>6.
%F (End)
%o (PARI) a(n) = {45^n - (8*n + 1)*9^n + 4*n*(8*n + 1)} \\ _Andrew Howroyd_, May 06 2020
%o (PARI) concat(0, Vec(16*x^2*(49 + 1341*x - 6093*x^2 - 6561*x^3) / ((1 - x)^3*(1 - 9*x)^2*(1 - 45*x)) + O(x^40))) \\ _Colin Barker_, Jul 19 2020
%Y Cf. A151624.
%K nonn,easy
%O 1,2
%A _R. H. Hardin_, May 29 2009
%E Terms a(7) and beyond from _Andrew Howroyd_, May 06 2020
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