A331433 Column 1 of triangle in A331431.

6, -24, 60, -120, 210, -336, 504, -720, 990, -1320, 1716, -2184, 2730, -3360, 4080, -4896, 5814, -6840, 7980, -9240, 10626, -12144, 13800, -15600, 17550, -19656, 21924, -24360, 26970, -29760, 32736, -35904, 39270, -42840, 46620, -50616, 54834, -59280, 63960, -68880, 74046

Offset: 0

Author

N. J. A. Sloane, Jan 17 2020

Keywords

• sign
• easy

Comments

Apart from the signs, essentially the same as A007531. - Georg Fischer, Jan 18 2020

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-4,-6,-4,-1)

Crossrefs

Cf. A000292, A007531, A331431.

Cf. A098737 (unsigned, 2nd subdiagonal).

Programs

Magma

[6*(-1)^n*Binomial(n+3,3): n in [0..50]]; // G. C. Greubel, Mar 22 2022

Mathematica

CoefficientList[Series[6/(1+x)^4, {x, 0, 40}], x] (* Georg Fischer, Jan 18 2020 *)

Sage

[6*(-1)^n*binomial(n+3,3) for n in (0..50)] # G. C. Greubel, Mar 22 2022

Formula

G.f.: 6/(1+x)^4. - Georg Fischer, Jan 18 2020

a(n) = 6*(-1)^n*A000292(n+1). - R. J. Mathar, Jan 21 2020

E.g.f.: (6 - 18*x + 9*x^2 - x^3)*exp(-x). - G. C. Greubel, Mar 22 2022

Extensions

a(4) changed to 210, and more terms from Georg Fischer, Jan 18 2020