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 A359647 #13 Aug 02 2023 09:23:36 %S A359647 1,6,140,4620,180180,7759752,356948592,17210021400,859544957700, %T A359647 44123307828600,2315270298060720,123691561681243920, %U A359647 6707888537328997200,368417878127146461600,20455964090297751153600,1146556787261188952159280,64797319609481605046295780 %N A359647 a(n) = [x^n] hypergeom([1/4, 3/4], [2], 64*x). The central terms of the Motzkin triangle A359364 without zeros. %C A359647 Number of Motzkin paths of length 4n with exactly 2n horizontal steps: a(1) = 6: UDHH, UHDH, UHHD, HUDH, HUHD, HHUD. - _Alois P. Heinz_, Aug 02 2023 %F A359647 a(n) = A359364(4*n, 2*n). %F A359647 a(n) = A000108(n) * A001448(n) = binomial(2*n,n)/(n+1)*binomial(4*n,2*n). - _Alois P. Heinz_, Aug 02 2023 %p A359647 ser := series(hypergeom([1/4, 3/4], [2], 64*x), x, 20): %p A359647 seq(coeff(ser, x, n), n = 0..16); %Y A359647 Cf. A000108, A001006, A001448, A359364. %K A359647 nonn %O A359647 0,2 %A A359647 _Peter Luschny_, Jan 09 2023