login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A287532 Square array read by antidiagonals: T(n,k) = sum of unimodal products of length n and bound k. 0
1, 1, 1, 1, 4, 1, 1, 11, 9, 1, 1, 26, 50, 16, 1, 1, 57, 222, 150, 25, 1, 1, 120, 867, 1080, 355, 36, 1, 1, 247, 3123, 6627, 3775, 721, 49, 1, 1, 502, 10660, 36552, 33502, 10626, 1316, 64, 1, 1, 1013, 35064, 187000, 262570, 128758, 25676, 2220, 81, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A unimodal product of length n and parameter k is a product of positive integers a_1 ... a_m ... a_n where a_1 <= ... <= a_m <= k and k >= a_m >= ... >= a_n; furthermore we consider each choice of m to give a distinct product, unless a_m=k. (See the example.)

LINKS

Table of n, a(n) for n=0..54.

FORMULA

T(n,k) is the coefficient of x^n in 1/((1-kx)(1-(k-1)x)^2...(1-x)^2).

EXAMPLE

T(2,3)=50 because of the products 1*1,1*1,1*1 [m=0,1,2]; 1*2,1*2 [m=1,2]; 1*3; 2*1,2*1 [m=0,1]; 2*2,2*2,2*2 [m=0,1,2]; 2*3; 3*1; 3*2; 3*3; total 50.

MATHEMATICA

f[k_]:=Product[1-j x, {j, k}]; T[n_, k_]:=Coefficient[Series[1/f[k]/f[k-1], {x, 0, n}], x, n]

CROSSREFS

Cf. A000290, A000295, A222993, A223069.

Sequence in context: A147564 A090981 A087903 * A112500 A152938 A154096

Adjacent sequences:  A287529 A287530 A287531 * A287533 A287534 A287535

KEYWORD

nonn,tabl

AUTHOR

Don Knuth, May 26 2017

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 March 26 20:47 EDT 2019. Contains 321535 sequences. (Running on oeis4.)