A285859
Number of permutations of [n] with eight ordered cycles such that equal-sized cycles are ordered with increasing least elements.
Original entry on oeis.org
1, 288, 19560, 921360, 37423914, 1124673264, 34065856396, 1010435626200, 27564092244689, 746494701977024, 20568917530438368, 575594436161070144, 15985318079107792576, 452561731064312392320, 12942265817549110947520, 383915932720263224659840
Offset: 8
-
b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
(p+n)!/n!*x^n, add(b(n-i*j, i-1, p+j)*(i-1)!^j*combinat
[multinomial](n, n-i*j, i$j)/j!^2*x^j, j=0..n/i)), x, 9)
end:
a:= n-> coeff(b(n$2, 0), x, 8):
seq(a(n), n=8..25);
-
multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, p_] := b[n, i, p] = Series[If[n == 0 || i == 1, (p + n)!/n!*x^n, Sum[b[n - i*j, i - 1, p + j]*(i - 1)!^j*multinomial[n, Join[{n - i*j}, Table[i, j]]]/j!^2*x^j, {j, 0, n/i}]], {x, 0, 9}];
a[n_] := Coefficient[b[n, n, 0], x, 8];
Table[a[n], {n, 8, 25}] (* Jean-François Alcover, May 30 2018, from Maple *)
A285860
Number of permutations of [n] with nine ordered cycles such that equal-sized cycles are ordered with increasing least elements.
Original entry on oeis.org
1, 405, 38610, 2331450, 121706442, 4694535846, 169670838480, 6075923190480, 198663468670953, 6325532235438273, 199912192325692002, 6415747810037718750, 203472294646893246264, 6508361104406113912344, 208391821362083355586128, 6837034161112760255699664
Offset: 9
-
b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
(p+n)!/n!*x^n, add(b(n-i*j, i-1, p+j)*(i-1)!^j*combinat
[multinomial](n, n-i*j, i$j)/j!^2*x^j, j=0..n/i)), x, 10)
end:
a:= n-> coeff(b(n$2, 0), x, 9):
seq(a(n), n=9..25);
-
multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, p_] := b[n, i, p] = Series[If[n == 0 || i == 1, (p + n)!/n!*x^n, Sum[b[n - i*j, i - 1, p + j]*(i - 1)!^j*multinomial[n, Join[{n - i*j}, Table[i, j]]]/j!^2*x^j, {j, 0, n/i}]], {x, 0, 10}];
a[n_] := Coefficient[b[n, n, 0], x, 9];
Table[a[n], {n, 9, 25}] (* Jean-François Alcover, May 30 2018, from Maple *)
A285861
Number of permutations of [n] with ten ordered cycles such that equal-sized cycles are ordered with increasing least elements.
Original entry on oeis.org
1, 550, 71225, 5448300, 355885530, 17364367020, 748875613200, 31800834780000, 1237174959934485, 46053097166277630, 1673378033771898675, 61000413008705597700, 2201843172941618228220, 79401490178154061870920, 2850407051830237872094980
Offset: 10
-
b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
(p+n)!/n!*x^n, add(b(n-i*j, i-1, p+j)*(i-1)!^j*combinat
[multinomial](n, n-i*j, i$j)/j!^2*x^j, j=0..n/i)), x, 11)
end:
a:= n-> coeff(b(n$2, 0), x, 10):
seq(a(n), n=10..25);
-
multinomial[n_, k_List] := n!/Times @@ (k!);
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}];
a[n_] := Coefficient[b[n, n, 0], x, 10];
Table[a[n], {n, 10, 25}] (* Jean-François Alcover, May 30 2018, from Maple *)