A334000 a(n) = (2*n+1)!! * Sum_{k=0..n} k/(2*k+1).

0, 1, 11, 122, 1518, 21423, 340869, 6058980, 119218860, 2575293165, 60628447215, 1545696702270, 42437227275450, 1248581232985275, 39197268410049225, 1307969571015966600, 46233376386927067800, 1725823391345415833625, 67845041198360981737875

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = (2*n+1)!!*(Sum_{k=0..n} k/(2*k+1)).

Recurrence: a(n) = 4*n*a(n-1)-(2*n-1)^2*a(n-2)+(2*n-1)!!.

Example

a(3) = 122 since 0/1 + 1/3 + 2/5 + 3/7 = 122/105 = 122/(7!!).

Mathematica

Table[Sum[k/(2*k+1), {k, 0, n}], {n, 0, 18}]*Table[Product[2*j+1, {j, 0, n}], {n, 0, 18}]
FullSimplify[Table[((n+1)/2 - HarmonicNumber[n + 1/2]/4 - Log[2]/2) * (2*n+1)!!, {n, 0, 20}]] (* Vaclav Kotesovec, Apr 14 2020 *)

Crossrefs

Cf. A004041.

Sequence in context: A288791 A049666 A163462 * A041222 A097708 A015499

Adjacent sequences: A333997 A333998 A333999 * A334001 A334002 A334003

Keyword

nonn,easy

Author

Greg Huber, Apr 11 2020

Status

approved