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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A156006 A symmetrical triangle based on A009799: a(n,m) = -(m - n)/(m + n)*Binomial[n + m, n]; t(n,m) = If[n == 0, 1, a(n, m) + a(n, n - m)] 0
1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 8, 10, 8, 1, 1, 18, 23, 23, 18, 1, 1, 47, 56, 56, 56, 47, 1, 1, 138, 152, 138, 138, 152, 138, 1, 1, 436, 456, 372, 330, 372, 456, 436, 1, 1, 1438, 1465, 1111, 847, 847, 1111, 1465, 1438, 1, 1, 4871, 4906, 3586, 2431, 2002, 2431, 3586 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 4, 10, 28, 84, 264, 858, 2860, 9724, 33592,...}.

LINKS

Table of n, a(n) for n=0..62.

FORMULA

a(n,m) = -(m - n)/(m + n)*Binomial[n + m, n];

t(n,m) = If[n == 0, 1, a(n, m) + a(n, n - m)]

EXAMPLE

{1},

{1, 1},

{1, 2, 1},

{1, 4, 4, 1},

{1, 8, 10, 8, 1},

{1, 18, 23, 23, 18, 1},

{1, 47, 56, 56, 56, 47, 1},

{1, 138, 152, 138, 138, 152, 138, 1},

{1, 436, 456, 372, 330, 372, 456, 436, 1},

{1, 1438, 1465, 1111, 847, 847, 1111, 1465, 1438, 1},

{1, 4871, 4906, 3586, 2431, 2002, 2431, 3586, 4906, 4871, 1}

MATHEMATICA

a[n_, m_] = -(m - n)/(m + n)*Binomial[n + m, n];

t[n_, m_] = If[n == 0, 1, a[n, m] + a[n, n - m]];

Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

A009799

Sequence in context: A126770 A202979 A306326 * A137854 A062715 A100631

Adjacent sequences:  A156003 A156004 A156005 * A156007 A156008 A156009

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 01 2009

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 June 24 17:58 EDT 2019. Contains 324330 sequences. (Running on oeis4.)