A343787
Number of ordered partitions of an n-set without blocks of size 4.
Original entry on oeis.org
1, 1, 3, 13, 74, 531, 4563, 45753, 524345, 6760039, 96837333, 1525909903, 26230304235, 488472319271, 9796281435125, 210496933103743, 4824574494068495, 117490079786298641, 3029472152485535343, 82454398253005541089, 2362311059301928969755, 71063998308414194250901
Offset: 0
Cf.
A000670,
A032032,
A337058,
A337059,
A343664,
A343788,
A343789,
A343790,
A343791,
A343792,
A343793.
-
a:= proc(n) option remember; `if`(n=0, 1, add(
`if`(j=4, 0, a(n-j)*binomial(n, j)), j=1..n))
end:
seq(a(n), n=0..21); # Alois P. Heinz, Apr 29 2021
-
nmax = 21; CoefficientList[Series[1/(2 + x^4/4! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 4, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]
A343788
Number of ordered partitions of an n-set without blocks of size 5.
Original entry on oeis.org
1, 1, 3, 13, 75, 540, 4671, 47125, 543371, 7048453, 101589591, 1610634433, 27856938387, 521953586233, 10532102378983, 227699187663961, 5250934660206219, 128659152359921997, 3337861722359261475, 91406502629924948053, 2634888477782107003707, 79751100251346500871481
Offset: 0
Cf.
A000670,
A032032,
A337058,
A337059,
A343665,
A343787,
A343789,
A343790,
A343791,
A343792,
A343793.
-
a:= proc(n) option remember; `if`(n=0, 1, add(
`if`(j=5, 0, a(n-j)*binomial(n, j)), j=1..n))
end:
seq(a(n), n=0..21); # Alois P. Heinz, Apr 29 2021
-
nmax = 21; CoefficientList[Series[1/(2 + x^5/5! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 5, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]
A343789
Number of ordered partitions of an n-set without blocks of size 6.
Original entry on oeis.org
1, 1, 3, 13, 75, 541, 4682, 47279, 545611, 7083565, 102182883, 1621425829, 28067555607, 526349480593, 10629883138059, 230009622202373, 5308749619032571, 130186940173803053, 3380385112758108315, 92650130825921846941, 2673020491585091254035, 80974418589343644492805
Offset: 0
Cf.
A000670,
A032032,
A337058,
A337059,
A343666,
A343787,
A343788,
A343790,
A343791,
A343792,
A343793.
-
a:= proc(n) option remember; `if`(n=0, 1, add(
`if`(j=6, 0, a(n-j)*binomial(n, j)), j=1..n))
end:
seq(a(n), n=0..21); # Alois P. Heinz, Apr 29 2021
-
nmax = 21; CoefficientList[Series[1/(2 + x^6/6! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 6, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]
A343790
Number of ordered partitions of an n-set without blocks of size 7.
Original entry on oeis.org
1, 1, 3, 13, 75, 541, 4683, 47292, 545819, 7086973, 102242283, 1622530933, 28089498891, 526813752973, 10640325166227, 230258631645913, 5315029292965675, 130353994525735677, 3385061859378821547, 92787606222541942477, 2677254928352340708075, 81110818086045534369661
Offset: 0
Cf.
A000670,
A032032,
A337058,
A337059,
A343667,
A343787,
A343788,
A343789,
A343791,
A343792,
A343793.
-
a:= proc(n) option remember; `if`(n=0, 1, add(
`if`(j=7, 0, a(n-j)*binomial(n, j)), j=1..n))
end:
seq(a(n), n=0..21); # Alois P. Heinz, Apr 29 2021
-
nmax = 21; CoefficientList[Series[1/(2 + x^7/7! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 7, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]
A343791
Number of ordered partitions of an n-set without blocks of size 8.
Original entry on oeis.org
1, 1, 3, 13, 75, 541, 4683, 47293, 545834, 7087243, 102247203, 1622625313, 28091415135, 526854986737, 10641264928479, 230281282588513, 5315605563021465, 130369438065006551, 3385496924633886429, 92800464391224494215, 2677652842774247060805, 81123688691904430522831
Offset: 0
Cf.
A000670,
A032032,
A337058,
A337059,
A343668,
A343787,
A343788,
A343789,
A343790,
A343792,
A343793.
-
a:= proc(n) option remember; `if`(n=0, 1, add(
`if`(j=8, 0, a(n-j)*binomial(n, j)), j=1..n))
end:
seq(a(n), n=0..21); # Alois P. Heinz, Apr 29 2021
-
nmax = 21; CoefficientList[Series[1/(2 + x^8/8! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 8, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]
A343792
Number of ordered partitions of an n-set without blocks of size 9.
Original entry on oeis.org
1, 1, 3, 13, 75, 541, 4683, 47293, 545835, 7087260, 102247543, 1622632133, 28091557915, 526858128161, 10641337741219, 230283060907913, 5315651289289195, 130370674248854021, 3385532005327322503, 92801507648842580769, 2677685300845992661475, 81124743440296074264381
Offset: 0
Cf.
A000670,
A032032,
A337058,
A337059,
A343669,
A343787,
A343788,
A343789,
A343790,
A343791,
A343793.
-
a:= proc(n) option remember; `if`(n=0, 1, add(
`if`(j=9, 0, a(n-j)*binomial(n, j)), j=1..n))
end:
seq(a(n), n=0..21); # Alois P. Heinz, Apr 29 2021
-
nmax = 21; CoefficientList[Series[1/(2 + x^9/9! - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[If[k == 9, 0, Binomial[n, k] a[n - k]], {k, 1, n}]]; Table[a[n], {n, 0, 21}]
Showing 1-6 of 6 results.