A331434 Column 2 of triangle in A331431.

30, -180, 630, -1680, 3780, -7560, 13860, -23760, 38610, -60060, 90090, -131040, 185640, -257040, 348840, -465120, 610470, -790020, 1009470, -1275120, 1593900, -1973400, 2421900, -2948400, 3562650, -4275180, 5097330, -6041280, 7120080, -8347680, 9738960

Offset: 0

Author

N. J. A. Sloane, Jan 17 2020

Keywords

• sign
• easy

Comments

Apart from the signs, essentially the same as A054559. - 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 (-6,-15,-20,-15,-6,-1).

Crossrefs

Cf. A000389, A054559, A331431.

Programs

Magma

[30*(-1)^n*Binomial(n+5, 5): n in [0..50]]; // G. C. Greubel, Mar 22 2022

Mathematica

CoefficientList[Series[30/(1+x)^6, {x, 0, 30}], x] (* Georg Fischer, Jan 18 2020 *)

Sage

[30*(-1)^n*binomial(n+5, 5) for n in (0..50)] # G. C. Greubel, Mar 22 2022

Formula

G.f.: 30/(1+x)^6. - Georg Fischer, Jan 18 2020

From G. C. Greubel, Mar 22 2022: (Start)

a(n) = 30*(-1)^n*binomial(n+5, 5).

a(n) = 30*(-1)^n*A000389(n+5).

E.g.f.: (1/4)*(120 - 600*x + 600*x^2 - 200*x^3 + 25*x^4 - x^5)*exp(-x). (End)

Extensions

a(0) changed to 30, and more terms from Georg Fischer, Jan 18 2020