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A151658
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Number of permutations of 8 indistinguishable copies of 1..n with exactly 2 adjacent element pairs in decreasing order.
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1
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0, 784, 73200, 3884640, 182107936, 8277726192, 373396825488, 16812327355840, 756652360885056, 34050346486482384, 1532275508306401840, 68952496159266606624, 3102863293076011859040, 139628857613659024861360, 6283298684030318768507856, 282748441663401954476011392
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = 45^n - (8*n + 1)*9^n + 4*n*(8*n + 1). - Andrew Howroyd, May 06 2020
G.f.: 16*x^2*(49 + 1341*x - 6093*x^2 - 6561*x^3) / ((1 - x)^3*(1 - 9*x)^2*(1 - 45*x)).
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.
(End)
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PROG
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(PARI) a(n) = {45^n - (8*n + 1)*9^n + 4*n*(8*n + 1)} \\ Andrew Howroyd, May 06 2020
(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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