A288790
Number of blocks of size >= eight in all set partitions of n.
Original entry on oeis.org
1, 10, 101, 947, 8670, 79249, 730745, 6838642, 65197797, 634656360, 6316333291, 64318009411, 670336612614, 7151290120037, 78085166445577, 872478836270306, 9972817907218608, 116575837400037486, 1393037460835481622, 17010118386233081680, 212160149063581345610
Offset: 8
-
b:= proc(n) option remember; `if`(n=0, 1, add(
b(n-j)*binomial(n-1, j-1), j=1..n))
end:
g:= proc(n, k) option remember; `if`(n g(n, 8):
seq(a(n), n=8..30);
-
Table[Sum[Binomial[n, j] BellB[j], {j, 0, n - 8}], {n, 8, 30}] (* Indranil Ghosh, Jul 06 2017 *)
-
from sympy import bell, binomial
def a(n): return sum(binomial(n, j)*bell(j) for j in range(n - 7))
print([a(n) for n in range(8, 31)]) # Indranil Ghosh, Jul 06 2017
A288791
Number of blocks of size >= nine in all set partitions of n.
Original entry on oeis.org
1, 11, 122, 1245, 12325, 121136, 1195147, 11915997, 120572790, 1241499241, 13030331671, 139549798524, 1525923634907, 17041290249637, 194394900237176, 2264977282222371, 26951265841776186, 327445918493429897, 4060993235341162405, 51396034231430455550
Offset: 9
-
b:= proc(n) option remember; `if`(n=0, 1, add(
b(n-j)*binomial(n-1, j-1), j=1..n))
end:
g:= proc(n, k) option remember; `if`(n g(n, 9):
seq(a(n), n=9..30);
-
Table[Sum[Binomial[n, j] BellB[j], {j, 0, n - 9}], {n, 9, 30}] (* Indranil Ghosh, Jul 06 2017 *)
-
from sympy import bell, binomial
def a(n): return sum([binomial(n, j)*bell(j) for j in range(n - 8)])
print([a(n) for n in range(9, 31)]) # Indranil Ghosh, Jul 06 2017
A288792
Number of blocks of size >= ten in all set partitions of n.
Original entry on oeis.org
1, 12, 145, 1600, 17032, 179132, 1883117, 19929390, 213332101, 2316793121, 25577181324, 287421068697, 3290394397097, 38393883291996, 456753452800691, 5540597439008861, 68530489547341697, 864218608315007230, 11109867095322262250, 145563654356205885737
Offset: 10
-
b:= proc(n) option remember; `if`(n=0, 1, add(
b(n-j)*binomial(n-1, j-1), j=1..n))
end:
g:= proc(n, k) option remember; `if`(n g(n, 10):
seq(a(n), n=10..30);
-
Table[Sum[Binomial[n, j] BellB[j], {j, 0, n - 10}], {n, 10, 30}] (* Indranil Ghosh, Jul 06 2017 *)
-
from sympy import bell, binomial
def a(n): return sum([binomial(n, j)*bell(j) for j in range(n - 9)])
print([a(n) for n in range(10, 31)]) # Indranil Ghosh, Jul 06 2017