A334670 a(n) = (2*n+1)!! * (Sum_{k=1..n} 1/(2*k+1)).

0, 1, 8, 71, 744, 9129, 129072, 2071215, 37237680, 741975345, 16236211320, 387182170935, 9995788416600, 277792140828825, 8269430130712800, 262542617405726175, 8855805158351474400, 316285840413064454625, 11924219190760084593000, 473245342972281190686375, 19722890048636406588957000

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..403

Formula

a(n) + A001147(n+1) = A004041(n).

a(n) = (2*n+1) * a(n-1) + A001147(n) for n>0.

P-finite with recurrence a(n) = 4*n*a(n-1) - (2*n-1)^2 * a(n-2) for n>1.

Example

a(1) = 3 * (1/3) = 1.
a(2) = 3*5 * (1/3 + 1/5) = 8.
a(3) = 3*5*7 * (1/3 +1/5 + 1/7) = 71.

Mathematica

a[n_] := (2*n + 1)!! * Sum[1/(2*k + 1), {k, 1, n}]; Array[a, 21, 0] (* Amiram Eldar, Apr 29 2021 *)

Prog

(PARI) {a(n) = prod(k=1, n, 2*k+1)*sum(k=1, n, 1/(2*k+1))}
(PARI) {a(n) = if(n<2, n, 4*n*a(n-1)-(2*n-1)^2*a(n-2))}

Crossrefs

Column k=1 of A335095.

Cf. A001147, A001705, A004041, A288875, A334000, A334066.

Sequence in context: A199687 A225033 A075506 * A094911 A294166 A203008

Adjacent sequences: A334667 A334668 A334669 * A334671 A334672 A334673

Keyword

nonn

Author

Seiichi Manyama, Sep 10 2020

Status

approved