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A285861 Number of permutations of [n] with ten ordered cycles such that equal-sized cycles are ordered with increasing least elements.

%I A285861 #13 May 30 2018 08:06:05
%S A285861 1,550,71225,5448300,355885530,17364367020,748875613200,
%T A285861 31800834780000,1237174959934485,46053097166277630,
%U A285861 1673378033771898675,61000413008705597700,2201843172941618228220,79401490178154061870920,2850407051830237872094980
%N A285861 Number of permutations of [n] with ten ordered cycles such that equal-sized cycles are ordered with increasing least elements.
%H A285861 Alois P. Heinz, <a href="/A285861/b285861.txt">Table of n, a(n) for n = 10..450</a>
%H A285861 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%p A285861 b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
%p A285861       (p+n)!/n!*x^n, add(b(n-i*j, i-1, p+j)*(i-1)!^j*combinat
%p A285861       [multinomial](n, n-i*j, i$j)/j!^2*x^j, j=0..n/i)), x, 11)
%p A285861     end:
%p A285861 a:= n-> coeff(b(n$2, 0), x, 10):
%p A285861 seq(a(n), n=10..25);
%t A285861 multinomial[n_, k_List] := n!/Times @@ (k!);
%t A285861 b[n_, i_, p_] := b[n, i, p] = Series[If[n == 0 || i == 1, (p + n)!/n!*x^n, Sum[b[n - i*j, i - 1, p + j]*(i - 1)!^j*multinomial[n, Join[{n - i*j}, Table[i, j]]]/j!^2*x^j, {j, 0, n/i}]], {x, 0, 11}];
%t A285861 a[n_] := Coefficient[b[n, n, 0], x, 10];
%t A285861 Table[a[n], {n, 10, 25}] (* _Jean-François Alcover_, May 30 2018, from Maple *)
%Y A285861 Column k=10 of A285849.
%Y A285861 Cf. A285925.
%K A285861 nonn
%O A285861 10,2
%A A285861 _Alois P. Heinz_, Apr 27 2017