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A335096 a(n) = ((2*n+1)!!)^n * (Sum_{k=1..n} 1/(2*k+1)^n). 2
0, 1, 34, 55511, 11575291716, 548347875819272649, 8811385079228718926321932614, 66303398534111438173105653188803948359375, 308529654991526005900670429792887300937160115962403125000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..8.

FORMULA

a(n) ~ 2^(n*(n + 3/2)) * n^(n*(n+1)) / (3^n * exp(n^2 - 11/24)). - Vaclav Kotesovec, Sep 25 2020

MATHEMATICA

Table[((2*n + 1)!!)^n * Sum[1/(2*k + 1)^n, {k, 1, n}], {n, 0, 10}] (* Vaclav Kotesovec, Sep 25 2020 *)

PROG

(PARI) {a(n) = prod(k=1, n, 2*k+1)^n*sum(k=1, n, 1/(2*k+1)^n)}

CROSSREFS

Main diagonal of A335095.

Cf. A291676.

Sequence in context: A270874 A222875 A180770 * A243314 A189649 A280901

Adjacent sequences:  A335093 A335094 A335095 * A335097 A335098 A335099

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Sep 12 2020

STATUS

approved

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Last modified January 29 05:07 EST 2022. Contains 350672 sequences. (Running on oeis4.)