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%I #7 Apr 20 2023 12:44:51
%S 1,45,1320,31680,677391,13462449,254795255,4662766680,83340628657,
%T 1465044247953,25454998074402,438717429420660,7520382153446728,
%U 128469777544339440,2190375675509324512,37315178727984493248,635733806304497380480,10838531804748912309760
%N Number of permutations of [n] having nine cycles of the form (c1, c2, ..., c_m) where c1 = min_{i>=1} c_i and c_j = min_{i>=j} c_i or c_j = max_{i>=j} c_i.
%H Alois P. Heinz, <a href="/A346324/b346324.txt">Table of n, a(n) for n = 9..805</a>
%H <a href="/index/Rec#order_45">Index entries for linear recurrences with constant coefficients</a>, signature (330, -52800, 5458112, -409849440, 23830243008, -1116839206912, 43364908274688, -1422999482800896, 40058156732292608, -978670938644226048, 20942693414834552832, -395446816019413024768, 6628468576745778216960, -99116218184391967899648, 1327508552532459972460544, -15978281861391727821520896, 173298921567278166366879744, -1697377642956536255696863232, 15039055418439163296689946624, -120693655145162007585780400128, 878147515604701507248361308160, -5795792475071168089051417804800, 34706940268381073600027534819328, -188551466825614090325337225297920, 928884554289456702023164149891072, -4146417475852344193885323361517568, 16752183792719693637308595161792512, -61164657351393624896479985594793984, 201430335115361975707349262702477312, -596910508818491373885524377560154112, 1587051894847366726188907145962979328, -3772628804072179811853984527214968832, 7984145251623466281818939408043212800, -14966672353343847363036369316837588992, 24697091814471831008013458269091659776, -35604534604039942742993725274323943424, 44426487522143027605937173809076371456, -47418685502140063487312346061511589888, 42644665320511517040368456880416096256, -31673648933874248884237267484421390336, 18900410135831532683919385850334412800, -8703688713240112875831154333188096000, 2901395900962149543887676333096960000, -622680424058111823400908777062400000, 64560982045934655213753964953600000).
%p b:= proc(n) option remember; series(`if`(n=0, 1, add(b(n-j)
%p *binomial(n-1, j-1)*x*ceil(2^(j-2)), j=1..n)), x, 10)
%p end:
%p a:= n-> coeff(b(n), x, 9):
%p seq(a(n), n=9..29);
%Y Column k=9 of A344855.
%K nonn,easy
%O 9,2
%A _Alois P. Heinz_, Jul 13 2021
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