This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A027972 #13 Sep 08 2022 08:44:49
%S A027972 1,4,11,29,76,199,518,1324,3278,7784,17643,38138,78753,155793,296248,
%T A027972 543333,964239,1660748,2783499,4550843,7273394,11385571,17485634,
%U A027972 26385946,39175444,57296576,82639259,117654736,165492559
%N A027972 T(n, 2n-10), T given by A027960.
%H A027972 G. C. Greubel, <a href="/A027972/b027972.txt">Table of n, a(n) for n = 5..1000</a>
%H A027972 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F A027972 Sequence satisfies a 10-degree polynomial approximating A002878.
%F A027972 G.f.: x^5*(1 -7*x +22*x^2 -37*x^3 +32*x^4 +x^5 -32*x^6 +37*x^7 -22*x^8 +7*x^9 -x^10)/(1-x)^11. - _R. J. Mathar_, Jan 30 2011
%F A027972 a(n) = -76 +183941*n/2520 +386899*n^3/36288 -1747657*n^2/50400 -831241*n^4/362880 +11887*n^5/34560 -5807*n^6/172800 +41*n^7/24192 +n^8/60480 -n^9/145152 +n^10/3628800. - _R. J. Mathar_, Jan 30 2011
%p A027972 seq(coeff(series(x^5*(1 -7*x +22*x^2 -37*x^3 +32*x^4 +x^5 -32*x^6 +37*x^7 -22*x^8 +7*x^9 -x^10)/(1-x)^11, x, n+1), x, n), n = 5..40); # _G. C. Greubel_, Sep 26 2019
%t A027972 Drop[CoefficientList[Series[x^5*(1 -7*x +22*x^2 -37*x^3 +32*x^4 +x^5 -32*x^6 +37*x^7 -22*x^8 +7*x^9 -x^10)/(1-x)^11, {x, 0, 40}], x], 5] (* _G. C. Greubel_, Sep 26 2019 *)
%o A027972 (PARI) my(x='x+O('x^40)); Vec(x^5*(1 -7*x +22*x^2 -37*x^3 +32*x^4 +x^5 -32*x^6 +37*x^7 -22*x^8 +7*x^9 -x^10)/(1-x)^11) \\ _G. C. Greubel_, Sep 26 2019
%o A027972 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x^5*(1- 7*x+22*x^2-37*x^3+32*x^4+x^5-32*x^6+37*x^7-22*x^8+7*x^9 -x^10)/(1-x)^11 )); // _G. C. Greubel_, Sep 26 2019
%o A027972 (Sage)
%o A027972 def A027972_list(prec):
%o A027972 P.<x> = PowerSeriesRing(ZZ, prec)
%o A027972 return P( x^5*(1 -7*x +22*x^2 -37*x^3 +32*x^4 +x^5 -32*x^6 +37*x^7 -22*x^8 +7*x^9 -x^10)/(1-x)^11 ).list()
%o A027972 a=A027972_list(40); a[5:] # _G. C. Greubel_, Sep 26 2019
%o A027972 (GAP) a:=[1, 4, 11, 29, 76, 199, 518, 1324, 3278, 7784, 17643];; for n in [12..40] do a[n]:=11*a[n-1]-55*a[n-2]+165*a[n-3]-330*a[n-4]+462*a[n-5] -462*a[n-6]+330*a[n-7]-165*a[n-8]+55*a[n-9]-11*a[n-10]+a[n-11]; od; a; # _G. C. Greubel_, Sep 26 2019
%Y A027972 A column of triangle A026998.
%K A027972 nonn
%O A027972 5,2
%A A027972 _Clark Kimberling_