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A378781
a(n) = n^3 * 2^n * binomial(3*n, n) / 3.
1
0, 2, 160, 6048, 168960, 4004000, 85542912, 1701719040, 32133218304, 583116019200, 10255365120000, 175853140869120, 2953078190899200, 48728661198077952, 792158036489666560, 12713192776728576000, 201760465448645689344, 3170643145439310643200, 49394436443159427809280
OFFSET
0,2
LINKS
D. V. Chudnovsky and G. V. Chudnovsky, Classification of hypergeometric identities for Pi and other logarithms of algebraic numbers, Proceedings of the National Academy of Sciences, Vol. 95, No. 6 (1998), pp. 2744-2749. See p. 2749.
FORMULA
a(n) = A128789(n) * A005809(n) / 3.
a(n) = n * A378778(n) / 3.
a(n) = n^2 * A378780(n) / 3.
Sum_{n>=1) 1/a(n) = 3*G*Pi - Pi^2*log(2)/8 + log(2)^3/2 - 99*zeta(3)/16, where G is Catalan's constant (Chudnovsky and Chudnovsky, 1998).
MATHEMATICA
a[n_] := n^3 * 2^n * Binomial[3*n, n] / 3; Array[a, 25, 0]
PROG
(PARI) a(n) = n^3 * 2^n * binomial(3*n, n) / 3;
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Dec 07 2024
STATUS
approved