A129464 Second column (m=1) of triangle A129462 (v=2 member of a certain family).

1, -2, -6, -48, -720, -17280, -604800, -29030400, -1828915200, -146313216000, -14485008384000, -1738201006080000, -248562743869440000, -41758540970065920000, -8142915489162854400000, -1824013069572479385600000, -465123332740982243328000000

Offset: 0

Author

Wolfdieter Lang, May 04 2007

Keywords

• sign
• easy

Comments

See A129462 for the M. Bruschi et al. reference.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A129462, A129465 (m=2), A129466 (m=3).

Cf. A229020.

Programs

Magma

[1] cat [-Factorial(n-1)*Factorial(n+1): n in [1..30]]; // G. C. Greubel, Feb 08 2024

Maple

A129464 := n -> `if`(n=0,1,-(n-1)!^2*n*(n+1)); # Peter Luschny, Oct 15 2010

Mathematica

Table[If[n==0, 1, -(n-1)!*(n+1)!], {n,0,30}] (* G. C. Greubel, Feb 08 2024 *)

SageMath

[1]+[-factorial(n-1)*factorial(n+1) for n in range(1,31)] # G. C. Greubel, Feb 08 2024

Formula

a(n) = A129462(n+1,1), n >= 0.

a(n) = -(n-1)!^2*n*(n+1), n > 0. - Peter Luschny, Oct 15 2010

From Amiram Eldar, May 17 2022: (Start)

Sum_{n>=1} 1/a(n) = -BesselI(2, 2) = -A229020.

Sum_{n>=1} (-1)^n/a(n) = BesselJ(2, 2). (End)