Voozh

A335090

a(n) = ((2*n+1)!!)^2 * (Sum_{k=1..n} 1/(2*k+1)^2).

0, 1, 34, 1891, 164196, 20760741, 3616621254, 832001250375, 244557191709000, 89472598178279625, 39886085958271670250, 21288783013213520392875, 13405493416599700058947500, 9835107221539462476348118125, 8316889511005794888839427108750, 8030850428074789829954674314399375

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..15.

FORMULA

a(n) = (8*n^2+2) * a(n-1) - (2*n-1)^4 * a(n-2) for n>1.

a(n) ~ (Pi^2/8 - 1) * 2^(2*n + 3) * n^(2*n + 2) / exp(2*n). - Vaclav Kotesovec, Sep 25 2020

MATHEMATICA

a[n_] := ((2*n + 1)!!)^2 * Sum[1/(2*k + 1)^2, {k, 1, n}]; Array[a, 16, 0] (* Amiram Eldar, Apr 29 2021 *)

PROG

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