1,2

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,...). A160701 = INVERT transform of the Bell sequence starting with

offset 0: (1, 1, 2, 5, 15, 52,...). (End)

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

Thomas Wieder, Home Page.

Thomas Wieder, (Old) Home Page.

a(n) = Sum_{i=1..n} Bell(i)*a(n-i).

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}.

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]

Cf. A000110, A055887, A083355.

A160701 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 24 2009]

Sequence in context: A129156 A002212 A149041 this_sequence A162162 A149042 A081921

Adjacent sequences: A129244 A129245 A129246 this_sequence A129248 A129249 A129250

nonn

Thomas Wieder (thomas.wieder(AT)t-online.de), May 10 2008

Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 25 2008