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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A173583 A q-form product triangle based on:q=5;a(n, q)= Sum[(1 + (-1)^n)*q^m, {m, 1, n}]/2 0
1, 1, 1, 1, 26, 1, 1, 651, 651, 1, 1, 16276, 407526, 16276, 1, 1, 406901, 254720026, 254720026, 406901, 1, 1, 10172526, 159200423151, 3980255126276, 159200423151, 10172526, 1, 1, 254313151, 99500274641901, 62191645548485651 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 28, 1304, 440080, 510253856, 4298676317632, 124582292154881408,

26237287231770008445184, 19009801643590721091612008960,

100087345880027826738936975715572736,...}.

These q are square like:

q = 2; A022168;

q = 3; A022173;

q = 4; A022180.

LINKS

Table of n, a(n) for n=0..31.

FORMULA

q=5;a(n, q)= Sum[(1 + (-1)^n)*q^m, {m, 1, n}]/2;

c(n,q)=Product[a(k, q), {k, 2, n, 2}];

t(n,m,q)=c(n, q)/(c(m, q)*c(n - m, q))

EXAMPLE

{1},

{1, 1},

{1, 26, 1},

{1, 651, 651, 1},

{1, 16276, 407526, 16276, 1},

{1, 406901, 254720026, 254720026, 406901, 1},

{1, 10172526, 159200423151, 3980255126276, 159200423151, 10172526, 1},

{1, 254313151, 99500274641901, 62191645548485651, 62191645548485651, 99500274641901, 254313151, 1},

{1, 6357828776, 62187671905501276, 971744561195362938776, 24293673734022755907526, 971744561195362938776, 62187671905501276, 6357828776, 1},

{1, 158945719401, 38867294947296126276, 15183508830865217823876276, 9489717274097200221740282526, 9489717274097200221740282526, 15183508830865217823876276, 38867294947296126276, 158945719401, 1},

{1, 3973642985026, 24292059342219024641901, 237242325521136323445362938776, 3706920825377727667482515685595026, 92673029744572745012632668283251276, 3706920825377727667482515685595026, 237242325521136323445362938776, 24292059342219024641901, 3973642985026, 1}

MATHEMATICA

a[n_, q_] := Sum[(1 + (-1)^n)*q^m, {m, 1, n}]/2;

c[n_, q_] := Product[a[k, q], {k, 2, n, 2}];

t[n_, m_, q_] := c[n, q]/(c[m, q]*c[n - m, q]);

Table[Table[Table[t[n, m, q], {m, 0, n, 2}], {n, 0, 20, 2}], {q, 1, 10}];

Table[Flatten[ Table[Table[t[n, m, q], {m, 0, n, 2}], {n, 0, 20, 2}]], {q, 1, 10}]

CROSSREFS

Sequence in context: A225483 A183065 A157630 * A040687 A040688 A040686

Adjacent sequences:  A173580 A173581 A173582 * A173584 A173585 A173586

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 22 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 15 13:54 EST 2019. Contains 329149 sequences. (Running on oeis4.)