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A282296 a(n) is the denominator of Sum_{k=0..n} Catalan(k)/(2^(2k)(n-k+1)^2). 2
1, 2, 144, 576, 57600, 4800, 7526400, 36126720, 6502809600, 6502809600, 899245670400, 3596982681600, 3404184409866240, 2836820341555200, 45389125464883200, 726226007438131200, 228959253981403545600, 20767279272689664, 1499397563488193740800, 67818905179312147660800, 2984031827889734497075200 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The series A282294(n)/a(n) is absolutely convergent to Pi^2/3.
It seems that each a(n)>1 is a product of primes p<=n+2.
LINKS
MATHEMATICA
a[n_]=Sum[CatalanNumber[k]/(2^(2k)(n-k+1)^2), {k, 0, n}]; Denominator /@a/@ Range[0, 20]
PROG
(PARI) C(n) = binomial(2*n, n)/(n+1);
a(n) = denominator(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), A282294 (numerators).
Sequence in context: A283097 A304582 A320061 * A163275 A157073 A304461
KEYWORD
nonn,frac
AUTHOR
Ralf Steiner, Feb 12 2017
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)