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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.

A369024 Expansion of (1/x) * Series_Reversion( x * (1-2*x)^4 / (1-x) ).

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%I A369024 #21 Jan 25 2024 11:16:30
%S A369024 1,7,81,1135,17617,291479,5038177,89901023,1643514849,30623478951,
%T A369024 579444828465,11103818394447,215053322179121,4202849976054583,
%U A369024 82778942956393409,1641477474636943295,32743892109730116801,656612555241354578759,13228883898856161274129
%N A369024 Expansion of (1/x) * Series_Reversion( x * (1-2*x)^4 / (1-x) ).
%H A369024 Seiichi Manyama, <a href="/A369024/b369024.txt">Table of n, a(n) for n = 0..749</a>
%H A369024 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369024 a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(4*n+k+3,k) * binomial(4*n+2,n-k).
%F A369024 D-finite with recurrence -2*(462919*n-251445)*(4*n+1) *(2*n+1)*(4*n+3) *(n+1)*a(n) +(625365036*n^5 +403579400*n^4 -437229300*n^3 +49132810*n^2 -20878971*n +3771675)*a(n-1) +(484851248*n^5 -3077382030*n^4 +7964893000*n^3 -10232074140*n^2 +6398384592*n -1533654945)*a(n-2) +(652184*n-451475)*(4*n-9) *(n-2)*(4*n-7)*(2*n-3)*a(n-3)=0. - _R. J. Mathar_, Jan 25 2024
%o A369024 (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-2*x)^4/(1-x))/x)
%o A369024 (PARI) a(n, s=1, t=4, u=-1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
%Y A369024 Cf. A344553, A369023.
%K A369024 nonn
%O A369024 0,2
%A A369024 _Seiichi Manyama_, Jan 12 2024