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A334670
a(n) = (2*n+1)!! * (Sum_{k=1..n} 1/(2*k+1)).
5
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
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.
Sequence in context: A199687 A225033 A075506 * A094911 A294166 A203008
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 10 2020
STATUS
approved