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 A064054 #30 Aug 18 2024 15:54:08
%S A064054 5,50,266,1016,3139,8350,19855,43252,87802,168168,306735,536640,
%T A064054 905658,1481108,2355962,3656360,5550755,8260934,12075184,17363896,
%U A064054 24597925,34370050,47419905,64662780,87222720,116470380,154066125,202008896,262691396,338962184
%N A064054 Tenth column of trinomial coefficients.
%H A064054 G. C. Greubel, <a href="/A064054/b064054.txt">Table of n, a(n) for n = 0..1000</a>
%H A064054 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F A064054 a(n) = A027907(n+5, 9).
%F A064054 a(n) = binomial(n+5, 5)*(n^4+66*n^3+1307*n^2+8706*n+15120) /(9!/5!).
%F A064054 G.f.: (1+x-x^2)*(5-5*x+x^2)/(1-x)^10, numerator polynomial is N3(9, x)= 5+0*x-9*x^2+6*x^3-x^4 from array A063420.
%F A064054 a(n) = A111808(n+5,9) for n>3. - _Reinhard Zumkeller_, Aug 17 2005
%F A064054 a(n) = 5*binomial(n+5,5) + 20*binomial(n+5,6) + 21*binomial(n+5,7) + 8*binomial(n+5,8) + binomial(n+5,9) (see our comment in A026729). - _Vladimir Shevelev_ and _Peter J. C. Moses_, Jun 22 2012
%F A064054 a(n) = GegenbauerC(N, -n, -1/2) where N = 9 if 9<n else 2*n-9. - _Peter Luschny_, May 10 2016
%p A064054 A064054 := n -> GegenbauerC(`if`(9<n,9,2*n-9), -n, -1/2):
%p A064054 seq(simplify(A064054(n)), n=5..20); # _Peter Luschny_, May 10 2016
%t A064054 Table[GegenbauerC[9, -n, -1/2], {n,5,50}] (* _G. C. Greubel_, Feb 28 2017 *)
%o A064054 (PARI) for(n=0,25, print1(binomial(n+5,5)*(n^4 + 66*n^3 + 1307*n^2 + 8706*n + 15120) /(9!/5!), ", ")) \\ _G. C. Greubel_, Feb 28 2017
%Y A064054 A005716 (ninth column), A111808.
%K A064054 nonn,easy
%O A064054 0,1
%A A064054 _Wolfdieter Lang_, Aug 29 2001