A332856
Number of entries in the seventh cycles of all permutations of [n] when cycles are ordered by decreasing lengths.
Original entry on oeis.org
1, 29, 583, 10366, 177299, 3029643, 52724894, 944353801, 17510885251, 337239557401, 6756438503137, 140893616636126, 3057901614671778, 69040616816923804, 1620394508763080044, 39500148841295346478, 999160362731046844470, 26200784568622019301658
Offset: 7
-
b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))((i-1)!^j*
b(n-i*j, min(n-i*j, i-1), max(0, t-j))/j!*
combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))
end:
a:= n-> b(n$2, 7)[2]:
seq(a(n), n=7..24);
A332857
Number of entries in the eighth cycles of all permutations of [n] when cycles are ordered by decreasing lengths.
Original entry on oeis.org
1, 37, 916, 19526, 392085, 7734663, 153275513, 3090075848, 63852563521, 1358480574137, 29837098126826, 677555150712614, 15919961048979164, 387124513859258764, 9741441909198136488, 253578333540120825224, 6825015749404715358362, 189819840262710177446426
Offset: 8
-
b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))((i-1)!^j*
b(n-i*j, min(n-i*j, i-1), max(0, t-j))/j!*
combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))
end:
a:= n-> b(n$2, 8)[2]:
seq(a(n), n=8..26);
A332858
Number of entries in the ninth cycles of all permutations of [n] when cycles are ordered by decreasing lengths.
Original entry on oeis.org
1, 46, 1376, 34662, 808029, 18239040, 408622073, 9219406943, 211361047584, 4951434599465, 118953031062221, 2937244849150543, 74649387584172199, 1954230833420758243, 52717076107348326739, 1465510610406405412331, 41979421676766533788251, 1238736596075658751908901
Offset: 9
-
b:= proc(n, l) option remember; `if`(n=0, l[9], add((j-1)!*b(n-j,
sort([l[], j], `>`)[1..9])*binomial(n-1, j-1), j=1..n))
end:
a:= n-> b(n, [0$9]):
seq(a(n), n=9..26);
-
b[n_, l_] := b[n, l] = If[n == 0, l[[9]], Sum[(j-1)! b[n-j, ReverseSort[ Append[l, j]][[1 ;; 9]]] Binomial[n - 1, j - 1], {j, 1, n}]];
a[n_] := b[n, Table[0, {9}]];
a /@ Range[9, 26] (* Jean-François Alcover, Mar 01 2020, after Alois P. Heinz *)
A332859
Number of entries in the tenth cycles of all permutations of [n] when cycles are ordered by decreasing lengths.
Original entry on oeis.org
1, 56, 1992, 58566, 1569387, 40210458, 1011778943, 25407870031, 643294838111, 16530707226038, 433032539982493, 11597633757170403, 318186179384754262, 8953723541105483282, 258628065642282683675, 7671629851218367059371, 233734404206144319940526
Offset: 10
-
b:= proc(n, l) option remember; `if`(n=0, l[10], add((j-1)!*b(n-j,
sort([l[], j], `>`)[1..10])*binomial(n-1, j-1), j=1..n))
end:
a:= n-> b(n, [0$10]):
seq(a(n), n=10..27);
-
b[n_, l_] := b[n, l] = If[n == 0, l[[10]], Sum[(j-1)!*b[n-j, ReverseSort[ Append[l, j]][[1 ;; 10]]] Binomial[n - 1, j - 1], {j, 1, n}]];
a[n_] := b[n, Table[0, {10}]];
a /@ Range[10, 27] (* Jean-François Alcover, Mar 01 2020, after Alois P. Heinz *)