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

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)}
(PARI) {a(n) = if(n<2, n, (8*n^2+2)*a(n-1)-(2*n-1)^4*a(n-2))}

Crossrefs

Column k=2 of A335095.

Cf. A001824, A334670, A335091, A335092.

Sequence in context: A086881 A212023 A056566 * A242177 A187591 A160471

Adjacent sequences: A335087 A335088 A335089 * A335091 A335092 A335093

Keyword

nonn

Author

Seiichi Manyama, Sep 11 2020

Status

approved