Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #18 Mar 23 2022 04:30:43
%S 30,-180,630,-1680,3780,-7560,13860,-23760,38610,-60060,90090,-131040,
%T 185640,-257040,348840,-465120,610470,-790020,1009470,-1275120,
%U 1593900,-1973400,2421900,-2948400,3562650,-4275180,5097330,-6041280,7120080,-8347680,9738960
%N Column 2 of triangle in A331431.
%C Apart from the signs, essentially the same as A054559. - _Georg Fischer_, Jan 18 2020
%H G. C. Greubel, <a href="/A331434/b331434.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-6,-15,-20,-15,-6,-1).
%F G.f.: 30/(1+x)^6. - _Georg Fischer_, Jan 18 2020
%F From _G. C. Greubel_, Mar 22 2022: (Start)
%F a(n) = 30*(-1)^n*binomial(n+5, 5).
%F a(n) = 30*(-1)^n*A000389(n+5).
%F E.g.f.: (1/4)*(120 - 600*x + 600*x^2 - 200*x^3 + 25*x^4 - x^5)*exp(-x). (End)
%t CoefficientList[Series[30/(1+x)^6, {x, 0, 30}], x] (* _Georg Fischer_, Jan 18 2020 *)
%o (Magma) [30*(-1)^n*Binomial(n+5, 5): n in [0..50]]; // _G. C. Greubel_, Mar 22 2022
%o (Sage) [30*(-1)^n*binomial(n+5, 5) for n in (0..50)] # _G. C. Greubel_, Mar 22 2022
%Y Cf. A000389, A054559, A331431.
%K sign,easy
%O 0,1
%A _N. J. A. Sloane_, Jan 17 2020
%E a(0) changed to 30, and more terms from _Georg Fischer_, Jan 18 2020