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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A282195 a(n) is the numerator of Sum_{m=0..n}(Sum_{k=0..m} ((k+1)/(m-k+1)^2) * (Catalan(k)/(2^(2*k)))^2)*(Sum_{k=0..n-m} ((k+1)/(n-m-k+1)^2) * (Catalan(k)/(2^(2*k)))^2)). 2
1, 3, 299, 1691, 4451729, 13446833, 16372396819, 208298035171, 1669160962863, 446401251163753, 6516008708737202119, 44233149340111747277, 5029067414956952883994601, 5810809342741928035310687, 46442062699559407155897191, 1018306138326248284055588777, 369103117042133718901423551221401 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The series a(n)/A282196(n) is absolutely convergent to (2/3 Pi)^2.

LINKS

Paolo P. Lava, Table of n, a(n) for n = 0..100

MAPLE

with(numtheory): P:=proc(q); numer(add(add((k+1)/(m-k+1)^2*((binomial(2*k, k)/(k+1))/(2^(2*k)))^2, k=0..m)*add((k+1)/(q-m-k+1)^2*((binomial(2*k, k)/(k+1))/(2^(2*k)))^2, k=0..q-m), m=0..q)); end: seq(P(i), i=0..100); # Paolo P. Lava, Feb 14 2017

MATHEMATICA

b[n_]=(Sum[((k+1)/(n-k+1)^2)((CatalanNumber[k])/(2^(2k)))^2, {k, 0, n}]); a[n_] = Sum[(b[k]*b[n - k]), {k, 0, n}]; Numerator /@a/@ Range[0, 10]

PROG

(PARI) C(n) = binomial(2*n, n)/(n+1);

b(n) = sum(k=0, n, ((k+1)/(n-k+1)^2) * (C(k)/(2^(2*k)))^2);

a(n) = numerator(sum(k=0, n, b(k)*b(n-k))); \\ Michel Marcus, Feb 11 2017

CROSSREFS

Cf. A281070, A280723, A282196 (denominators).

Cf. A000108 (Catalan), A019693 (2 Pi/3).

Sequence in context: A212798 A157579 A104821 * A303388 A119065 A119069

Adjacent sequences:  A282192 A282193 A282194 * A282196 A282197 A282198

KEYWORD

nonn,frac

AUTHOR

Ralf Steiner, Feb 08 2017

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 October 18 07:00 EDT 2018. Contains 316307 sequences. (Running on oeis4.)