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 A360047 #17 Jan 25 2023 08:34:49
%S A360047 1,5,15,35,70,127,220,385,715,1430,3005,6400,13500,28050,57800,119515,
%T A360047 250425,533525,1151975,2504700,5453176,11856275,25748450,55962300,
%U A360047 121981725,266968938,586630515,1292992795,2855288480,6311930460,13963767356,30919563310
%N A360047 a(n) = Sum_{k=0..floor(n/5)} binomial(n+4,5*k+4) * Catalan(k).
%H A360047 Seiichi Manyama, <a href="/A360047/b360047.txt">Table of n, a(n) for n = 0..1000</a>
%F A360047 a(n) = binomial(n+4,4) + Sum_{k=0..n-5} a(k) * a(n-k-5).
%F A360047 G.f. A(x) satisfies: A(x) = 1/(1-x)^5 + x^5 * A(x)^2.
%F A360047 G.f.: 2 / ( (1-x)^2 * ((1-x)^3 + sqrt((1-x)^6 - 4*x^5*(1-x))) ).
%F A360047 D-finite with recurrence (n+5)*a(n) +6*(-n-4)*a(n-1) +15*(n+3)*a(n-2) +20*(-n-2)*a(n-3) +15*(n+1)*a(n-4) +10*(-n+1)*a(n-5) +5*(n-1)*a(n-6)=0. - _R. J. Mathar_, Jan 25 2023
%o A360047 (PARI) a(n) = sum(k=0, n\5, binomial(n+4, 5*k+4)*binomial(2*k, k)/(k+1));
%o A360047 (PARI) my(N=40, x='x+O('x^N)); Vec(2/((1-x)^2*((1-x)^3+sqrt((1-x)^6-4*x^5*(1-x)))))
%Y A360047 Cf. A086615, A360045, A360046.
%Y A360047 Cf. A000108.
%K A360047 nonn
%O A360047 0,2
%A A360047 _Seiichi Manyama_, Jan 23 2023