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 A358092 #14 Oct 30 2022 03:06:26 %S A358092 1,1,3,9,28,88,279,889,2843,9115,29279,94183,303294,977522,3152709, %T A358092 10173671,32844544,106073200,342671109,1107278239,3578704532, %U A358092 11568322736,37400611581,120931966547,391065616195,1264729338163,4090528413309,13230930776769,42798305388298 %N A358092 Row sums of the convolution triangle of the Motzkin numbers (A202710). %F A358092 a(n) = [x^n] (sqrt(x + 1)*(1 - 2*x) + sqrt(1 - 3*x)) / (sqrt(x + 1)*(1 - 4*x) + sqrt(1 - 3*x)). %F A358092 a(n) = ((36-12*n)*a(n-4) + (30-14*n)*a(n-3) + (3*n-3)*a(n-2) + (4*n-3)*a(n-1))/n for n >= 5. %p A358092 ogf := (sqrt(x + 1)*(1 - 2*x) + sqrt(1 - 3*x)) / (sqrt(x + 1)*(1 - 4*x) + sqrt(1 - 3*x)): ser := series(ogf, x, 32): seq(coeff(ser, x, n), n = 0..28); %p A358092 # Alternatively: %p A358092 a := proc(n) option remember; ifelse(n < 5, [1, 1, 3, 9, 28][n + 1], %p A358092 ((36-12*n)*a(n-4) + (30-14*n)*a(n-3) + (3*n-3)*a(n-2) + a(n-1)*(4*n-3))/n) end: %p A358092 seq(a(n), n = 0..28); %Y A358092 Cf. A202710, A001006. %K A358092 nonn %O A358092 0,3 %A A358092 _Peter Luschny_, Oct 29 2022