login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A188685 Partial alternating sums of binomial(3n,n)^2/(2n+1)^2. 10
1, 0, 9, 135, 2890, 71639, 1967545, 58125959, 1813561210, 59034994415, 1987910416810, 68818255912790, 2437897047570874, 88061136002276310, 3234416650430634090, 120525771933269446806, 4548292982313797644875 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..608

FORMULA

a(n) = Sum_{k=0..n} (-1)^(n-k)*A001764(k)^2.

4*(2*n^2 + 9*n + 10)^2*a(n+2) - (713*n^4 + 4230*n^3 + 9317*n^2 + 9000*n + 3200)*a(n+1) - 9*(9*n^2 + 27*n + 20)^2*a(n) = 0.

a(n) ~ 3^(6*n+7)/(745*Pi*n^3*2^(4*n+4)). - Vaclav Kotesovec, Aug 06 2013

MAPLE

A001764 := proc(n) binomial(3*n, n)/(2*n+1) ; end proc:

A188685 := proc(n) add( (-1)^(n-k)*A001764(k)^2, k=0..n) ; end proc: # R. J. Mathar, Apr 11 2011

MATHEMATICA

Table[Sum[Binomial[3k, k]^2(-1)^(n-k)/(2k+1)^2, {k, 0, n}], {n, 0, 20}]

PROG

(Maxima) makelist(sum(binomial(3*k, k)^2*(-1)^(n-k)/(2k+1)^2, k, 0, n), n, 0, 20);

(MAGMA) [ &+[(-1)^(n-k)*Binomial(3*k, k)^2/(2*k+1)^2: k in [0..n]]: n in [0..16]];  // Bruno Berselli, Apr 11 2011

CROSSREFS

Cf. A001764, A005809, A104859, A188678, A188681.

Cf. Alternate partial sums of binomial(3n,n)^2/(2n+1)^k: A188680 (k=0), A188683 (k=1), this sequence (k=2).

Sequence in context: A235339 A306848 A034723 * A052137 A003376 A253879

Adjacent sequences:  A188682 A188683 A188684 * A188686 A188687 A188688

KEYWORD

nonn,easy

AUTHOR

Emanuele Munarini, Apr 08 2011

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 September 29 21:59 EDT 2020. Contains 337432 sequences. (Running on oeis4.)