A285924
Number of ordered set partitions of [n] into nine blocks such that equal-sized blocks are ordered with increasing least elements.
Original entry on oeis.org
1, 405, 37125, 1738935, 64914993, 1775214441, 38186115825, 751359827790, 13076544824343, 207877406991111, 3041686131983343, 41512373437449915, 544051964769008601, 6850772610392201733, 82608610920666732693, 956263706215482795570, 10851693841665124551180
Offset: 9
-
b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
(p+n)!/n!*x^n, add(x^j*b(n-i*j, i-1, p+j)*combinat
[multinomial](n, n-i*j, i$j)/j!^2, j=0..n/i)), x, 10)
end:
a:= n-> coeff(b(n$2, 0), x, 9):
seq(a(n), n=9..30);
-
multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, p_] := b[n, i, p] = Series[If[n == 0 || i == 1, (p + n)!/n!*x^n, Sum[x^j*b[n - i*j, i - 1, p + j]*multinomial[n, Join[{n - i*j}, Table[i, j]]]/j!^2, {j, 0, n/i}]], {x, 0, 10}];
a[n_] := Coefficient[b[n, n, 0], x, 9];
Table[a[n], {n, 9, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)
A285925
Number of ordered set partitions of [n] into ten blocks such that equal-sized blocks are ordered with increasing least elements.
Original entry on oeis.org
1, 550, 69025, 4254250, 201371170, 7180042870, 196518086050, 4766802769300, 102889172957285, 2006511403380770, 36104901766271975, 597121503366547250, 9381072363234242330, 140940747710164417070, 2033219852450765548790, 28025263737301449789500
Offset: 10
-
b:= proc(n, i, p) option remember; series(`if`(n=0 or i=1,
(p+n)!/n!*x^n, add(x^j*b(n-i*j, i-1, p+j)*combinat
[multinomial](n, n-i*j, i$j)/j!^2, j=0..n/i)), x, 11)
end:
a:= n-> coeff(b(n$2, 0), x, 10):
seq(a(n), n=10..30);
-
multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, p_] := b[n, i, p] = Series[If[n == 0 || i == 1, (p + n)!/n!*x^n, Sum[x^j*b[n - i*j, i - 1, p + j]*multinomial[n, Join[{n - i*j}, Table[i, j]]]/j!^2, {j, 0, n/i}]], {x, 0, 11}];
a[n_] := Coefficient[b[n, n, 0], x, 10];
Table[a[n], {n, 10, 30}] (* Jean-François Alcover, May 17 2018, translated from Maple *)
A285926
Number of ordered set partitions of [2n] into n blocks such that equal-sized blocks are ordered with increasing least elements.
Original entry on oeis.org
1, 1, 11, 420, 17129, 1049895, 97141022, 10742461730, 1370094506209, 207877406991111, 36104901766271975, 7033373902938469086, 1531762189401458287506, 368890302956243012167470, 97283928918541409263666020, 27895730515878936009534815250
Offset: 0
-
b:= proc(n, i, p) option remember; expand(`if`(n=0 or i=1,
(p+n)!/n!*x^n, add(x^j*b(n-i*j, i-1, p+j)*combinat
[multinomial](n, n-i*j, i$j)/j!^2, j=0..n/i)))
end:
a:= n-> coeff(b(2*n$2, 0), x, n):
seq(a(n), n=0..20);
-
multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, p_] := b[n, i, p] = Expand[If[n == 0 || i == 1, (p + n)!/n! x^n, Sum[b[n - i j, i - 1, p + j] x^j multinomial[n, Join[{n - i j}, Table[i, j]]]/j!^2, {j, 0, n/i}]]];
a[n_] := Coefficient[b[2n, 2n, 0], x, n];
a /@ Range[0, 20] (* Jean-François Alcover, Dec 08 2020, after Alois P. Heinz *)