|
| |
|
|
A129247
|
|
Invert transform of the Bell numbers.
|
|
3
| |
|
|
1, 3, 10, 36, 138, 560, 2402, 10898, 52392, 267394, 1450790, 8371220, 51327178, 333759746, 2295276480, 16639104002, 126718172670, 1010487248556, 8411744415418, 72899055533482, 656136245454232, 6120474697035762
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| The following definition of the invert transform leads to the understanding of A129247 [M. Bernstein & N. J. A. Sloane, Some canonical sequences of integers, Linear Algebra and its Applications, 226-228 (1995), 57-72]: "b_n is the number of ordered arrangements of postage stamps of total value n that can be formed if we have a_i types of stamps of value i, i >= 1."
Hankel transform is A000178. [From Paul Barry (pbarry(AT)wit.ie), Jan 08 2009]
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), May 24 2009: (Start)
A129247 = INVERT transform of the Bell sequence starting with offset 1:
(1, 2, 5,...). A137551 = INVERT transform of the Bell sequence starting with
offset 0: (1, 1, 2, 5, 15, 52,...). (End)
|
|
|
LINKS
| M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210.
N. J. A. Sloane, Transforms
|
|
|
FORMULA
| a(n) = Sum_{i=1..n} Bell(i)*a(n-i).
|
|
|
EXAMPLE
| We have Bell(i) types of an integer i with i=1,2,...,n, where Bell(i) is the i-th Bell number.
We write i_j for integer i of type j.
a(2)=3 because
{1_1,1_1}
{2_1}, {2_2}.
a(3)=10 because
{1_1,1_1,1_1},
{1_1,2_1}, {2_1,1_1},
{1_1,2_2}, {2_2,1_1}
{3_1}, {3_2}, {3_3}, {3_4}, {3_5}.
|
|
|
MAPLE
| A129247 := proc(n) option remember ; local i ; if n <= 1 then 1 ; else add(combinat[bell](i)*procname(n-i), i=1..n) ; fi ; end: for n from 1 to 40 do printf("%d, ", A129247(n)) ; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 25 2008]
|
|
|
CROSSREFS
| Cf. A000110, A055887, A083355.
Sequence in context: A002212 A149041 A202834 * A162162 A149042 A081921
Adjacent sequences: A129244 A129245 A129246 * A129248 A129249 A129250
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Thomas Wieder (thomas.wieder(AT)t-online.de), May 10 2008
|
|
|
EXTENSIONS
| Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 25 2008
|
| |
|
|
