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A282294 a(n) is the numerator of Sum_{k=0..n} Catalan(k)/(2^(2k)(n-k+1)^2). 2
1, 1, 43, 115, 8279, 523, 645707, 2512261, 375022771, 316811893, 37578099073, 130584316861, 108534879071711, 80175074314547, 1146376386895811, 16508128877802479, 4713666134111655121, 389384452277345, 25732651148411424601, 1070142416759689230289, 43469649877346464376879 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The series a(n)/A282296(n) is absolutely convergent to Pi^2/3.

LINKS

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

MAPLE

with(numtheory): P:=proc(q) local k;

numer(add((binomial(2*k, k)/(k+1))/(2^(2*k)*(q-k+1)^2), k=0..q));

end: seq(P(i), i=0..100); # Paolo P. Lava, Feb 14 2017

MATHEMATICA

a[n_]=Sum[CatalanNumber[k]/(2^(2k)(n-k+1)^2), {k, 0, n}]; Numerator /@a/@ Range[0, 20]

PROG

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

a(n) = numerator(sum(k=0, n, C(k)/(2^(2*k)*(n-k+1)^2))); \\ Michel Marcus, Feb 12 2017

CROSSREFS

Cf. A000108 (Catalan), A195055 (Pi^2/3), A282296 (denominators).

Sequence in context: A142081 A138695 A297412 * A251075 A248018 A262491

Adjacent sequences:  A282291 A282292 A282293 * A282295 A282296 A282297

KEYWORD

nonn,frac

AUTHOR

Ralf Steiner, Feb 12 2017

STATUS

approved

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Last modified November 23 17:41 EST 2020. Contains 338595 sequences. (Running on oeis4.)