A162994 The third left hand column of triangle A162990.

64, 1600, 57600, 2822400, 180633600, 14631321600, 1463132160000, 177038991360000, 25493614755840000, 4308420893736960000, 844450495172444160000, 190001361413799936000000, 48640348521932783616000000, 14057060722838574465024000000, 4554487674199698126667776000000

Offset

3,1

Links

Table of n, a(n) for n=3..17.

Formula

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

a(n) = A002301(n+1)^2.

From Amiram Eldar, Feb 27 2026: (Start)

Sum_{n>=3} 1/a(n) = 9 * BesselI(0, 2) - 41/2 = 9 * A070910 - 41/2.

Sum_{n>=3} (-1)^(n+1)/a(n) = 9 * BesselJ(0, 2) - 2 = 9 * A091681 - 2. (End)

Mathematica

Array[((#+1)!/3)^2 &, 20, 3] (* Paolo Xausa, Apr 01 2024 *)

Crossrefs

A001044 and A162993 are two other left hand columns.

A002301(n+1) equals the square root of a(n).

Cf. A070910, A091681.

Sequence in context: A014794 A224282 A224205 * A225981 A232427 A194496

Adjacent sequences: A162991 A162992 A162993 * A162995 A162996 A162997

Keyword

easy,nonn

Author

Johannes W. Meijer, Jul 21 2009

Status

approved