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A285860 Number of permutations of [n] with nine ordered cycles such that equal-sized cycles are ordered with increasing least elements.

%I A285860 #13 May 30 2018 07:18:08
%S A285860 1,405,38610,2331450,121706442,4694535846,169670838480,6075923190480,
%T A285860 198663468670953,6325532235438273,199912192325692002,
%U A285860 6415747810037718750,203472294646893246264,6508361104406113912344,208391821362083355586128,6837034161112760255699664
%N A285860 Number of permutations of [n] with nine ordered cycles such that equal-sized cycles are ordered with increasing least elements.
%H A285860 Alois P. Heinz, <a href="/A285860/b285860.txt">Table of n, a(n) for n = 9..450</a>
%H A285860 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%p A285860 b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
%p A285860       (p+n)!/n!*x^n, add(b(n-i*j, i-1, p+j)*(i-1)!^j*combinat
%p A285860       [multinomial](n, n-i*j, i$j)/j!^2*x^j, j=0..n/i)), x, 10)
%p A285860     end:
%p A285860 a:= n-> coeff(b(n$2, 0), x, 9):
%p A285860 seq(a(n), n=9..25);
%t A285860 multinomial[n_, k_List] := n!/Times @@ (k!);
%t A285860 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, 10}];
%t A285860 a[n_] := Coefficient[b[n, n, 0], x, 9];
%t A285860 Table[a[n], {n, 9, 25}] (* _Jean-François Alcover_, May 30 2018, from Maple *)
%Y A285860 Column k=9 of A285849.
%Y A285860 Cf. A285924.
%K A285860 nonn
%O A285860 9,2
%A A285860 _Alois P. Heinz_, Apr 27 2017