A261065 Second column of A086872.

1, 8, 75, 840, 11025, 166320, 2837835, 54054000, 1137161025, 26189163000, 655383804075, 17709112020600, 513880482740625, 15938200818540000, 526174085058496875, 18422283260401020000, 681816379418800250625, 26597171457203972625000, 1090705672840839577396875

Offset

1,2

Links

Table of n, a(n) for n=1..19.

Formula

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

G.f.: x*3F1(3/2,4,2; 3; 2x).

a(n) = A001879(n-1) + 2*A001880(n+2).

From Amiram Eldar, Jul 11 2026: (Start)

a(n) = (n+2) * (2*n)!/(3 * 2^n * (n-1)!).

a(n) ~ 2^(n+1/2) * n^(n+2) / (3*exp(n)).

E.g.f.: -x*(x-1)/(1-2*x)^(5/2). (End)

Mathematica

a[n_] := (n+2) * (2*n)!/(3 * 2^n * (n-1)!); Array[a, 19] (* Amiram Eldar, Jul 11 2026 *)

Crossrefs

Cf. A001879, A001880, A086872.

Sequence in context: A383951 A067306 A361528 * A071720 A391313 A273998

Adjacent sequences: A261062 A261063 A261064 * A261066 A261067 A261068

Keyword

nonn,easy,changed

Author

R. J. Mathar, Aug 08 2015

Status

approved