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Column 1 of triangle in A331431.
3

%I #25 Mar 23 2022 07:38:19

%S 6,-24,60,-120,210,-336,504,-720,990,-1320,1716,-2184,2730,-3360,4080,

%T -4896,5814,-6840,7980,-9240,10626,-12144,13800,-15600,17550,-19656,

%U 21924,-24360,26970,-29760,32736,-35904,39270,-42840,46620,-50616,54834,-59280,63960,-68880,74046

%N Column 1 of triangle in A331431.

%C Apart from the signs, essentially the same as A007531. - _Georg Fischer_, Jan 18 2020

%H G. C. Greubel, <a href="/A331433/b331433.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-4,-6,-4,-1)

%F G.f.: 6/(1+x)^4. - _Georg Fischer_, Jan 18 2020

%F a(n) = 6*(-1)^n*A000292(n+1). - _R. J. Mathar_, Jan 21 2020

%F E.g.f.: (6 - 18*x + 9*x^2 - x^3)*exp(-x). - _G. C. Greubel_, Mar 22 2022

%t CoefficientList[Series[6/(1+x)^4, {x, 0, 40}], x] (* _Georg Fischer_, Jan 18 2020 *)

%o (Magma) [6*(-1)^n*Binomial(n+3,3): n in [0..50]]; // _G. C. Greubel_, Mar 22 2022

%o (Sage) [6*(-1)^n*binomial(n+3,3) for n in (0..50)] # _G. C. Greubel_, Mar 22 2022

%Y Cf. A000292, A007531, A331431.

%Y Cf. A098737 (unsigned, 2nd subdiagonal).

%K sign,easy

%O 0,1

%A _N. J. A. Sloane_, Jan 17 2020

%E a(4) changed to 210, and more terms from _Georg Fischer_, Jan 18 2020