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%I #16 Jul 02 2023 18:51:16
%S 1,20,380,7201,136440,2585160,48981601,928065260,17584258340,
%T 333172843201,6312699762480,119608122643920,2266241630472001,
%U 42938982856324100,813574432639685900,15414975237297708001
%N Partial sums of Chebyshev sequence S(n,19)= U(n,19/2)=A078368(n).
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (20, -20, 1).
%F 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 G.f.: 1/((1-x)*(1-19*x+x^2)) = 1/(1-20*x+20*x^2-x^3).
%F 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 a(n) = 19*a(n-1)-a(n-2)+1, n>=1, a(-1)=0, a(0)=1.
%F a(n) = (S(n+1, 19) - S(n, 19) -1)/17.
%Y Cf. A212336 for more sequences with g.f. of the type 1/(1-k*x+k*x^2-x^3).
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Aug 31 2004
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