login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A209406 Triangular array read by rows: T(n,k) is the number of multisets of exactly k nonempty binary words with a total of n letters. 6
2, 4, 3, 8, 8, 4, 16, 26, 12, 5, 32, 64, 44, 16, 6, 64, 164, 132, 62, 20, 7, 128, 384, 376, 200, 80, 24, 8, 256, 904, 1008, 623, 268, 98, 28, 9, 512, 2048, 2632, 1792, 870, 336, 116, 32, 10, 1024, 4624, 6624, 5040, 2632, 1117, 404, 134, 36, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Equivalently, T(n,k) is the number of partitions of the integer n with two types of 1's, four types of 2's, ..., 2^i types of i's...; having exactly k summands (of any type).

Row sums = A034899.

LINKS

Alois P. Heinz, Rows n = 1..141, flattened

Index entries for triangles generated by the Multiset Transformation

FORMULA

O.g.f.: Product_{i>=1} 1/(1-y*x^i)^(2^i).

EXAMPLE

:   2;

:   4,    3;

:   8,    8,    4;

:  16,   26,   12,    5;

:  32,   64,   44,   16,   6;

:  64,  164,  132,   62,  20,   7;

: 128,  384,  376,  200,  80,  24,   8;

: 256,  904, 1008,  623, 268,  98,  28,  9;

: 512, 2048, 2632, 1792, 870, 336, 116, 32, 10;

MAPLE

b:= proc(n, i, p) option remember; `if`(p>n, 0, `if`(n=0, 1,

      `if`(min(i, p)<1, 0, add(b(n-i*j, i-1, p-j)*

       binomial(2^i+j-1, j), j=0..min(n/i, p)))))

    end:

T:= (n, k)-> b(n$2, k):

seq(seq(T(n, k), k=1..n), n=1..14);  # Alois P. Heinz, Apr 13 2017

MATHEMATICA

nn = 10; p[x_, y_] := Product[1/(1 - y x^i)^(2^i), {i, 1, nn}]; f[list_] := Select[lst, # > 0 &]; Map[f, Drop[CoefficientList[Series[p[x, y], {x, 0, nn}], {x, y}], 1]] // Flatten

CROSSREFS

Cf. A034899, A208741, A290222, A292506.

Sequence in context: A067179 A318993 A188843 * A188706 A304408 A048767

Adjacent sequences:  A209403 A209404 A209405 * A209407 A209408 A209409

KEYWORD

nonn,tabl

AUTHOR

Geoffrey Critzer, Mar 08 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 8 14:52 EDT 2020. Contains 333314 sequences. (Running on oeis4.)