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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A089722 Triangle T(n,k), 0<=k<=n, read by rows, defined by: Product{k=1..n, (1+x^k)^(n+1-k)} = Sum{k>=0, T(n,k)*x^k}. 0
1, 1, 1, 1, 2, 2, 2, 1, 1, 3, 5, 8, 10, 10, 10, 8, 5, 3, 1, 1, 4, 9, 18, 31, 46, 64, 82, 96, 106, 110, 106, 96, 82, 64, 46, 31, 18, 9, 4, 1, 1, 5, 14, 33, 68, 124, 210, 332, 492, 693, 931, 1196, 1476, 1754, 2008, 2220, 2374, 2453, 2453, 2374, 2220, 2008, 1754, 1476, 1196 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..64.

FORMULA

T(n, k) = Sum {a_1, a_2, ...a_n with a_1+2*a_2+...+n*a_n=k, C(n, a_1)*C(n-1, a_2)*...*C(1, a_n)} .

Sum_{k, k>=0} T(n, k) = 2^(n*(n+1)/2), see A006125.

EXAMPLE

Row n=0 : 1

Row n=1 : 1, 1

Row n=2 : 1, 2, 2, 2, 1

Row n=3 : 1, 3, 5, 8, 10, 10, 10, 8, 5, 3, 1

Row n=4 : 1, 4, 9, 18, 31, 46, 64, 82, 96, 106, 110, 106, 96, 82, 64, 46, 31, 18, 9, 4, 1

CROSSREFS

Cf. A006125.

Sequence in context: A193884 A128084 A131823 * A172356 A184948 A242775

Adjacent sequences:  A089719 A089720 A089721 * A089723 A089724 A089725

KEYWORD

easy,nonn,tabf

AUTHOR

Philippe Deléham, Jan 06 2004, Oct 16 2008

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 21 07:23 EDT 2019. Contains 321367 sequences. (Running on oeis4.)