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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.

%I A346325 #7 Apr 20 2023 12:46:11
%S A346325 1,55,1925,54340,1352351,31025995,673378420,14053611000,285145815097,
%T A346325 5667829234067,110975742044635,2149132308825320,41289962312119268,
%U A346325 788820616410896784,15011983120207453072,284985824919909766400,5402570836503080377280,102360869570893587962880
%N 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.
%H A346325 Alois P. Heinz, <a href="/A346325/b346325.txt">Table of n, a(n) for n = 10..778</a>
%H A346325 <a href="/index/Rec#order_55">Index entries for linear recurrences with constant coefficients</a>, 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).
%p A346325 b:= proc(n) option remember; series(`if`(n=0, 1, add(b(n-j)
%p A346325       *binomial(n-1, j-1)*x*ceil(2^(j-2)), j=1..n)), x, 11)
%p A346325     end:
%p A346325 a:= n-> coeff(b(n), x, 10):
%p A346325 seq(a(n), n=10..29);
%Y A346325 Column k=10 of A344855.
%K A346325 nonn,easy
%O A346325 10,2
%A A346325 _Alois P. Heinz_, Jul 13 2021