A106436 -id:A106436 - cp's OEIS frontend

A011967 4th differences of Bell numbers.

4, 15, 67, 322, 1657, 9089, 52922, 325869, 2114719, 14418716, 103004851, 769052061, 5987339748, 48506099635, 408157244967, 3561086589202, 32164670915029, 300324194090773, 2894932531218482, 28773297907499129

Offset: 0

N. J. A. Sloane

nonn

Chai Wah Wu, Table of n, a(n) for n = 0..250
Cohn, Martin; Even, Shimon; Menger, Karl, Jr.; Hooper, Philip K.; On the Number of Partitionings of a Set of n Distinct Objects, Amer. Math. Monthly 69 (1962), no. 8, 782--785. MR1531841.
Cohn, Martin; Even, Shimon; Menger, Karl, Jr.; Hooper, Philip K.; On the Number of Partitionings of a Set of n Distinct Objects, Amer. Math. Monthly 69 (1962), no. 8, 782--785. MR1531841. [Annotated scanned copy]
Jocelyn Quaintance and Harris Kwong, A combinatorial interpretation of the Catalan and Bell number difference tables, Integers, 13 (2013), #A29.

Cf. A000110, A005493, A011965, A011966, A106436.

Differences[BellB[Range[0, 50]], 4] (* Vladimir Joseph Stephan Orlovsky, May 25 2011 *)

# requires python 3.2 or higher. Otherwise use def'n of accumulate in python docs.
from itertools import accumulate
A011967_list, blist, b = [4], [5, 7, 10, 15], 15
for _ in range(250):
    blist = list(accumulate([b]+blist))
    b = blist[-1]
    A011967_list.append(blist[-5]) # Chai Wah Wu, Sep 20 2014

A182930 Triangle read by rows: Number of set partitions of {1,2,..,n} such that |k| is a block and no block |m| with m < k exists, (1 <= n, 1 <= k <= n).

Original entry on oeis.org

1, 1, 0, 2, 1, 1, 5, 3, 2, 1, 15, 10, 7, 5, 4, 52, 37, 27, 20, 15, 11, 203, 151, 114, 87, 67, 52, 41, 877, 674, 523, 409, 322, 255, 203, 162, 4140, 3263, 2589, 2066, 1657, 1335, 1080, 877, 715, 21147, 17007, 13744, 11155, 9089, 7432, 6097, 5017, 4140, 3425

Offset: 1

Peter Luschny, Apr 08 2011

Mirror image of A106436. - Alois P. Heinz, Jan 29 2019

			T(4,2) = card({2|134, 2|3|14, 2|4|13}) = 3.
[1]     1,
[2]     1,    0,
[3]     2,    1,    1,
[4]     5,    3,    2,    1,
[5]    15,   10,    7,    5,    4,
[6]    52,   37,   27,   20,   15,   11,
     [-1-] [-2-] [-3-] [-4-] [-5-] [-6-]

Alois P. Heinz, Rows n = 1..141, flattened
Peter Luschny, Set partitions

Cf. A000110, A000296, A106436.

T(2n+1,n+1) gives A020556.

T := proc(n, k) option remember; if n = 1 then 1 elif n = k then T(n-1,1) - T(n-1,n-1) else T(n-1,k) + T(n, k+1) fi end:
A182930 := (n,k) -> T(n,k); seq(print(seq(A182930(n,k),k=1..n)),n=1..6);

T[n_, k_] := T[n, k] = Which[n == 1, 1, n == k, T[n-1, 1] - T[n-1, n-1], True, T[n-1, k] + T[n, k+1]];
Table[T[n, k], {n, 1, 10}, {k, 1, n}] (* Jean-François Alcover, Jun 22 2019 *)

Recursion: The value of T(n,k) is, if n < 0 or k < 0 or k > n undefined, else if n = 1 then 1 else if k = n then T(n-1,1) - T(n-1,n-1); in all other cases T(n,k) = T(n,k+1) + T(n-1,k).

A191099 5th differences of Bell numbers.

Original entry on oeis.org

11, 52, 255, 1335, 7432, 43833, 272947, 1788850, 12303997, 88586135, 666047210, 5218287687, 42518759887, 359651145332, 3152929344235, 28603584325827, 268159523175744, 2594608337127709, 25878365376280647, 265770087291261082, 2807571511844891521

Offset: 0

Vladimir Joseph Stephan Orlovsky, May 25 2011

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..500
Jocelyn Quaintance and Harris Kwong, A combinatorial interpretation of the Catalan and Bell number difference tables, Integers, 13 (2013), #A29.

Cf. A000110, A005493, A011965, A011966, A011967, A106436.

Mathematica
```
Differences[BellB[Range[0, 50]], 5]
```

cp's OEIS Frontend

A011967 4th differences of Bell numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Python

A182930 Triangle read by rows: Number of set partitions of {1,2,..,n} such that |k| is a block and no block |m| with m < k exists, (1 <= n, 1 <= k <= n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A191099 5th differences of Bell numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica