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 A349362 #15 Nov 20 2021 07:19:38
%S A349362 1,1,5,40,370,3740,40006,445231,5102165,59799505,713496815,8637432580,
%T A349362 105826926716,1309793896431,16351672606365,205665994855320,
%U A349362 2603696877136060,33151784577226295,424258396639960591,5454120586840761631,70402732493668027775
%N A349362 G.f. A(x) satisfies: A(x) = 1 + x * A(x)^6 / (1 + x).
%H A349362 Seiichi Manyama, <a href="/A349362/b349362.txt">Table of n, a(n) for n = 0..500</a>
%F A349362 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,k-1) * binomial(6*k,k) / (5*k+1).
%F A349362 a(n) = (-1)^(n+1)* F([7/6, 4/3, 3/2, 5/3, 11/6, 1-n], [7/5, 8/5, 9/5, 2, 11/5], 6^6/5^5), where F is the generalized hypergeometric function. - _Stefano Spezia_, Nov 15 2021
%F A349362 a(n) ~ 43531^(n + 1/2) / (72 * sqrt(3*Pi) * n^(3/2) * 5^(5*n + 3/2)). - _Vaclav Kotesovec_, Nov 17 2021
%p A349362 a:= n-> coeff(series(RootOf(1+x*A^6/(1+x)-A, A), x, n+1), x, n):
%p A349362 seq(a(n), n=0..20); # _Alois P. Heinz_, Nov 15 2021
%t A349362 nmax = 20; A[_] = 0; Do[A[x_] = 1 + x A[x]^6/(1 + x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A349362 Table[Sum[(-1)^(n - k) Binomial[n - 1, k - 1] Binomial[6 k, k]/(5 k + 1), {k, 0, n}], {n, 0, 20}]
%Y A349362 Cf. A001006, A002295, A127897, A317133, A346065 (binomial transform), A346666, A349333, A349361, A349363, A349364.
%K A349362 nonn
%O A349362 0,3
%A A349362 _Ilya Gutkovskiy_, Nov 15 2021