A346324
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.
Original entry on oeis.org
1, 45, 1320, 31680, 677391, 13462449, 254795255, 4662766680, 83340628657, 1465044247953, 25454998074402, 438717429420660, 7520382153446728, 128469777544339440, 2190375675509324512, 37315178727984493248, 635733806304497380480, 10838531804748912309760
Offset: 9
- Alois P. Heinz, Table of n, a(n) for n = 9..805
- Index entries for linear recurrences with constant coefficients, 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).
-
b:= proc(n) option remember; series(`if`(n=0, 1, add(b(n-j)
*binomial(n-1, j-1)*x*ceil(2^(j-2)), j=1..n)), x, 10)
end:
a:= n-> coeff(b(n), x, 9):
seq(a(n), n=9..29);
A346325
Number of permutations of [n] having ten 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.
Original entry on oeis.org
1, 55, 1925, 54340, 1352351, 31025995, 673378420, 14053611000, 285145815097, 5667829234067, 110975742044635, 2149132308825320, 41289962312119268, 788820616410896784, 15011983120207453072, 284985824919909766400, 5402570836503080377280, 102360869570893587962880
Offset: 10
- Alois P. Heinz, Table of n, a(n) for n = 10..778
- Index entries for linear recurrences with constant coefficients, signature (440, -94380, 13153712, -1339466128, 106260979968, -6837719858112, 366926680184064, -16754270024524032, 660958303600637952, -22797958064717282304, 694101047140891865088, -18798159004470926462976, 455770979137970585075712, -9945563578803933661937664, 196204176974938968881430528, -3512596097523682019345104896, 57251367187054384747894013952, -851860730228923738649851592704, 11598053393743162392951592583168, -144773531270969031440371861684224, 1659581101562987607049435602747392, -17494821348650285028452211217137664, 169788894877154021979988488055947264, -1518394498375601327639809937721262080, 12520721694429294326935189405455876096, -95246662070290288708467946711846748160, 668603158974285744806395386200756060160, -4331385199788394747580964336937753116672, 25893247651679702584679386815842450669568, -142800383203446373407520728720765087645696, 726199874664276467991123081234787873062912, -3403175276702848465576438151974914908749824, 14683987389337524000218580196407402968383488, -58273737733136895062769874733039886884929536, 212426638444081222128029032421955355092713472, -710201535435080151470330314762738085033672704, 2173700391953770480907406854490275007690702848, -6077668535180062394584204166408239648862109696, 15485086612758079074333487993978542112775340032, -35848600044063055784725059727673653371653324800, 75153230245847013750160580121260867422695456768, -142111165732393085617810205746445864038727417856, 241270480938416107014190967553239071230812749824, -365763312657344636433179776533061910779649851392, 491906647608349119457835284380199229292948750336, -582281340590549964543758094633072346669177110528, 600847127582075778559692434659798409313597259776, -534014306886641306375699639546672366158029520896, 402556271892812081435559654644284793410792980480, -252227239123539880014648060573980723913110323200, 127753349105912267966186603448407159105126400000, -50233454686520977912143128647828024747622400000, 14380599628166470522133626131450645027225600000, -2665144771510709905052441335025922736128000000, 239901585047846581083822477336190648320000000).
-
b:= proc(n) option remember; series(`if`(n=0, 1, add(b(n-j)
*binomial(n-1, j-1)*x*ceil(2^(j-2)), j=1..n)), x, 11)
end:
a:= n-> coeff(b(n), x, 10):
seq(a(n), n=10..29);