A129465 Third column (m=2) sequence of triangle A129462 (v=2 member of a certain family).

1, 1, -4, -204, -7776, -358560, -20839680, -1516112640, -135920332800, -14772931891200, -1917601910784000, -293337284308992000, -52263416690343936000, -10734227287227924480000, -2518467729187335045120000, -669569466986357627289600000

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, A129464 (m=1), A129466(m=3).

Programs

Magma

A129465:= func< n | n eq 0 select 1 else -Factorial(n)*Factorial(n+2)*(HarmonicNumber(n+2) -2) >;
[A129465(n): n in [0..30]]; // G. C. Greubel, Feb 08 2024

Mathematica

A129465[n_]:= If[n==0, 1, -n!*(n+2)!*(HarmonicNumber[n+2] -2)];
Table[A129465[n], {n,0,30}] (* G. C. Greubel, Feb 08 2024 *)

SageMath

def A129465(n): return 1 if (n==0) else -factorial(n)*factorial(n+2)*( harmonic_number(n+2) -2)
[A129465(n) for n in range(31)] # G. C. Greubel, Feb 08 2024

Formula

a(n) = A129462(n+2, 2), n >= 0.

a(n) = (-1)*n!*(n+2)!*(HarmonicNumber(n+2) - 2), for n >= 1, otherwise a(0) = 1. - G. C. Greubel, Feb 08 2024