A285366
Sum of the entries in the fourth blocks of all set partitions of [n].
Original entry on oeis.org
4, 55, 495, 3757, 26421, 180482, 1230737, 8520912, 60531347, 444006008, 3374292280, 26605751388, 217686862402, 1847108846441, 16237616979723, 147709622593855, 1388722474550671, 13477574785475778, 134861358322272607, 1389822348657508142, 14735739124218384875
Offset: 4
-
a:= proc(h) option remember; local b; b:=
proc(n, m) option remember;
`if`(n=0, [1, 0], add((p-> `if`(j=4, p+ [0,
(h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
end: b(h, 0)[2]
end:
seq(a(n), n=4..30);
-
a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 4, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
Table[a[n], {n, 4, 30}] (* Jean-François Alcover, May 27 2018, from Maple *)
A285367
Sum of the entries in the fifth blocks of all set partitions of [n].
Original entry on oeis.org
5, 96, 1148, 11122, 96454, 787959, 6250696, 49115820, 387561065, 3100950735, 25330467332, 212222629466, 1828990798243, 16241051507536, 148696716804278, 1403754413149792, 13658941220426754, 136899626339091133, 1412247058871264298, 14982353645545370808
Offset: 5
-
a:= proc(h) option remember; local b; b:=
proc(n, m) option remember;
`if`(n=0, [1, 0], add((p-> `if`(j=5, p+ [0,
(h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
end: b(h, 0)[2]
end:
seq(a(n), n=5..30);
-
a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 5, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
Table[a[n], {n, 5, 30}] (* Jean-François Alcover, May 27 2018, from Maple *)
A285368
Sum of the entries in the sixth blocks of all set partitions of [n].
Original entry on oeis.org
6, 154, 2380, 28975, 308127, 3018824, 28133574, 254715640, 2274064881, 20242054046, 181155397430, 1640541610028, 15107388580258, 141982420633882, 1365335004650614, 13456694682282849, 136069364339492065, 1412201447170038064, 15044059353340996950
Offset: 6
-
a:= proc(h) option remember; local b; b:=
proc(n, m) option remember;
`if`(n=0, [1, 0], add((p-> `if`(j=6, p+ [0,
(h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
end: b(h, 0)[2]
end:
seq(a(n), n=6..30);
-
a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 6, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
Table[a[n], {n, 6, 30}] (* Jean-François Alcover, May 27 2018, from Maple *)
A285369
Sum of the entries in the seventh blocks of all set partitions of [n].
Original entry on oeis.org
7, 232, 4518, 67898, 875365, 10228471, 111964040, 1173487986, 11959590504, 119889568676, 1192711559418, 11859084564254, 118526150123309, 1196311505171568, 12239696866561282, 127315711586330538, 1349476206629576995, 14599608027440148129, 161399084259928978190
Offset: 7
-
a:= proc(h) option remember; local b; b:=
proc(n, m) option remember;
`if`(n=0, [1, 0], add((p-> `if`(j=7, p+ [0,
(h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
end: b(h, 0)[2]
end:
seq(a(n), n=7..30);
-
a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 7, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
Table[a[n], {n, 7, 30}] (* Jean-François Alcover, May 27 2018, from Maple *)
A285370
Sum of the entries in the eighth blocks of all set partitions of [n].
Original entry on oeis.org
8, 333, 7995, 145814, 2250020, 31075944, 397434249, 4813480830, 56089581910, 636257739216, 7090058863984, 78176548855068, 858005254659222, 9419825826737075, 103885234357070729, 1154951013922367450, 12982852258320087936, 147928345019800310188
Offset: 8
-
a:= proc(h) option remember; local b; b:=
proc(n, m) option remember;
`if`(n=0, [1, 0], add((p-> `if`(j=8, p+ [0,
(h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
end: b(h, 0)[2]
end:
seq(a(n), n=8..30);
-
a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 8, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
Table[a[n], {n, 8, 30}] (* Jean-François Alcover, May 27 2018, from Maple *)
A285371
Sum of the entries in the ninth blocks of all set partitions of [n].
Original entry on oeis.org
9, 460, 13365, 291312, 5313419, 85887795, 1273861815, 17739276489, 235727269842, 3025136223480, 37838768653358, 464684701656546, 5636371498958757, 67862072916294706, 814494099000392487, 9780912755503955712, 117894823818639390505, 1430383074839724093993
Offset: 9
-
a:= proc(h) option remember; local b; b:=
proc(n, m) option remember;
`if`(n=0, [1, 0], add((p-> `if`(j=9, p+ [0,
(h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
end: b(h, 0)[2]
end:
seq(a(n), n=9..30);
-
a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 9, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
Table[a[n], {n, 9, 30}] (* Jean-François Alcover, May 27 2018, from Maple *)
A285372
Sum of the entries in the tenth blocks of all set partitions of [n].
Original entry on oeis.org
10, 616, 21318, 547857, 11676343, 218761153, 3732864275, 59392240551, 895833879036, 12967143328027, 181820930739504, 2487908867278337, 33420903985242540, 442951837401015291, 5816787707500820380, 75959640100454216760, 989568067595589010921
Offset: 10
-
a:= proc(h) option remember; local b; b:=
proc(n, m) option remember;
`if`(n=0, [1, 0], add((p-> `if`(j=10, p+ [0,
(h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
end: b(h, 0)[2]
end:
seq(a(n), n=10..30);
-
a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 10, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
Table[a[n], {n, 10, 30}] (* Jean-François Alcover, May 27 2018, from Maple *)