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

 

Logo

The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A176021 A symmetrical triangle sequence:t(n,m)=1 - (-1)^n - (-1)^ n* n! + ((-1)^n* Binomial[ -1 + n, -1 + m] Binomial[ n, -1 + m] n!/(m*m!)) + ((-1)^n* Binomial[ -1 + n, -m + n] Binomial[n, -m + n] n!)/((1 - m + n) ( 1 - m + n)!) 0
1, 1, 1, 1, -10, 1, 1, 72, 72, 1, 1, -528, -678, -528, 1, 1, 4770, 6780, 6780, 4770, 1, 1, -48025, -87568, -68458, -87568, -48025, 1, 1, 524384, 1287776, 947520, 947520, 1287776, 524384, 1, 1, -6169282, -19982590, -18010942, -10305790, -18010942 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are:

{1, 2, -8, 146, -1732, 23102, -339642, 5519362, -98631416, 1926628022,...}.

LINKS

Table of n, a(n) for n=1..42.

FORMULA

t(n,m)=1 - (-1)^n - (-1)^ n* n! + ((-1)^n* Binomial[ -1 + n, -1 + m] Binomial[ n, -1 + m] n!/(m*m!)) + ((-1)^n* Binomial[ -1 + n, -m + n] Binomial[n, -m + n] n!)/((1 - m + n) ( 1 - m + n)!)

EXAMPLE

{1},

{1, 1},

{1, -10, 1},

{1, 72, 72, 1},

{1, -528, -678, -528, 1},

{1, 4770, 6780, 6780, 4770, 1},

{1, -48025, -87568, -68458, -87568, -48025, 1},

{1, 524384, 1287776, 947520, 947520, 1287776, 524384, 1},

{1, -6169282, -19982590, -18010942, -10305790, -18010942, -19982590, -6169282, 1},

{1, 78019650, 323011800, 379209600, 183072960, 183072960, 379209600, 323011800, 78019650, 1}

MATHEMATICA

L[n_, m_] = 1 - (-1)^n - (-1)^ n* n! + ((-1)^n* Binomial[ -1 + n, -1 + m] Binomial[ n, -1 + m] n!/(m*m!)) + ((-1)^n* Binomial[ -1 + n, -m + n] Binomial[n, -m + n] n!)/((1 - m + n) ( 1 - m + n)!);

Table[Table[L[n, m], {m, 1, n}], {n, 1, 10}];

Flatten[%]

CROSSREFS

Cf. A008297

Sequence in context: A142459 A157641 A129274 * A166972 A160562 A176243

Adjacent sequences:  A176018 A176019 A176020 * A176022 A176023 A176024

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Apr 06 2010

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 26 07:30 EDT 2017. Contains 287093 sequences.