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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A261398 Integer coefficients arising from a formula for Sum_{m>=1} sin(Pi*m/3)^2/m^2. 2
1, 2, 6, 32, 230, 2112, 23548, 309248, 4675014, 79969280, 1527092468, 32203259904, 743288515164, 18638209056768, 504541774904760, 14664951970922496, 455522635895576646, 15058911973677465600, 527896878148304296900, 19559986314930028544000, 763820398700983273655796, 31353195811771939838492672 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n)/(2^n*(n-1)!) = A049330(n)/A049331(n).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

J. W. H. Swanepoel, On a generalization of a theorem by Euler, Journal of Number Theory 149 (2015) 46-56.

FORMULA

a(n) = Sum_{i=0..[(n-1)/2]} (-1)^i*binomial(n,i)*(n-2*i)^(n-1).

a(n) = n * A099765(n). - Vladimir Reshetnikov, Sep 05 2016

MAPLE

A261398 := proc(n)

    add( (-1)^i*binomial(n, i)*(n-2*i)^(n-1), i=0..floor((n-1)/2)) ;

end proc:

seq(A261398(n), n=1..25) ; # R. J. Mathar, Aug 19 2015

MATHEMATICA

Table[Sum[(-1)^k (n-2k)^(n-1) Binomial[n, k], {k, 0, n/2}], {n, 1, 20}] (* Vladimir Reshetnikov, Sep 05 2016 *)

PROG

(PARI) a(n) = sum(i=0, (n-1)\2, (-1)^i*binomial(n, i)*(n-2*i)^(n-1)); \\ Michel Marcus, Sep 05 2016

CROSSREFS

Cf. A049330, A049331.

Sequence in context: A224884 A321086 A111550 * A009686 A012318 A012521

Adjacent sequences:  A261395 A261396 A261397 * A261399 A261400 A261401

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 18 2015

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 August 26 03:27 EDT 2019. Contains 326324 sequences. (Running on oeis4.)