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 A097832 #16 Jul 02 2023 18:51:16 %S A097832 1,20,380,7201,136440,2585160,48981601,928065260,17584258340, %T A097832 333172843201,6312699762480,119608122643920,2266241630472001, %U A097832 42938982856324100,813574432639685900,15414975237297708001 %N A097832 Partial sums of Chebyshev sequence S(n,19)= U(n,19/2)=A078368(n). %H A097832 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a> %H A097832 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (20, -20, 1). %F A097832 a(n) = sum(S(k, 19), k=0..n) with S(k, 19) = U(k, 19/2) = A078368(k) Chebyshev's polynomials of the second kind. %F A097832 G.f.: 1/((1-x)*(1-19*x+x^2)) = 1/(1-20*x+20*x^2-x^3). %F A097832 a(n) = 20*a(n-1)-20*a(n-2)+a(n-3), n>=2, a(-1)=0, a(0)=1, a(1)=20. %F A097832 a(n) = 19*a(n-1)-a(n-2)+1, n>=1, a(-1)=0, a(0)=1. %F A097832 a(n) = (S(n+1, 19) - S(n, 19) -1)/17. %Y A097832 Cf. A212336 for more sequences with g.f. of the type 1/(1-k*x+k*x^2-x^3). %K A097832 nonn,easy %O A097832 0,2 %A A097832 _Wolfdieter Lang_, Aug 31 2004